3.69.77 $\int \frac{300x-100x^2+e^x(-60+20x)+e^{3x}(-6x-3x^2-5x^3+2x^4)+e^{2x}(55x^3+15x^4-10x^5)+(e^{3x}(6+6x+10x^2-4x^3)+e^{2x}(-70x^2-40x^3+20x^4))\log (\frac{e^x(-3+x)+15x-5x^2}{x})+(e^{3x}(-3-5x+2x^2)+e^{2x}(15x+25x^2-10x^3)){\log }^2(\frac{e^x(-3+x)+15x-5x^2}{x})}{300x-100x^2+e^x(-60+20x)}dx$

Optimal. Leaf size=37 $$x+\frac{1}{20}{e}^{2x}x{(-x+\log \left(\frac{(3-x)(-e^x+5x)}{x}\right))}^2$$

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Rubi [F]  time = 53.69, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.000, Rules used = {} $$\begin{array}{c}\int \frac{300x-100x^2+e^x(-60+20x)+e^{3x}(-6x-3x^2-5x^3+2x^4)+e^{2x}(55x^3+15x^4-10x^5)+(e^{3x}(6+6x+10x^2-4x^3)+e^{2x}(-70x^2-40x^3+20x^4))\log \left(\frac{e^x(-3+x)+15x-5x^2}{x}\right)+(e^{3x}(-3-5x+2x^2)+e^{2x}(15x+25x^2-10x^3)){\log }^2\left(\frac{e^x(-3+x)+15x-5x^2}{x}\right)}{300x-100x^2+e^x(-60+20x)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(300*x - 100*x^2 + E^x*(-60 + 20*x) + E^(3*x)*(-6*x - 3*x^2 - 5*x^3 + 2*x^4) + E^(2*x)*(55*x^3 + 15*x^4 -
10*x^5) + (E^(3*x)*(6 + 6*x + 10*x^2 - 4*x^3) + E^(2*x)*(-70*x^2 - 40*x^3 + 20*x^4))*Log[(E^x*(-3 + x) + 15*x
- 5*x^2)/x] + (E^(3*x)*(-3 - 5*x + 2*x^2) + E^(2*x)*(15*x + 25*x^2 - 10*x^3))*Log[(E^x*(-3 + x) + 15*x - 5*x^2
)/x]^2)/(300*x - 100*x^2 + E^x*(-60 + 20*x)),x]

[Out]

(-13*E^x)/2 + (7*E^(2*x))/40 - (67*x)/8 + (27*E^x*x)/8 - (E^(2*x)*x)/40 - (15*x^2)/8 - (3*E^x*x^2)/4 + (E^(2*x
)*x^3)/20 - (5*x^4)/48 - x^5/8 - (E^6*ExpIntegralEi[-2*(3 - x)])/8 - (3*E^3*ExpIntegralEi[-3 + x])/2 + (3*ExpI
ntegralEi[x])/2 - ExpIntegralEi[2*x]/40 + (3*E^6*(3 - x)*ExpIntegralEi[-6 + 2*x])/10 - (225*Log[3 - x])/8 + (3
*E^x*Log[-(((E^x - 5*x)*(3 - x))/x)])/2 - (E^(2*x)*Log[-(((E^x - 5*x)*(3 - x))/x)])/40 - (3*E^x*x*Log[-(((E^x
- 5*x)*(3 - x))/x)])/2 + (E^(2*x)*x*Log[-(((E^x - 5*x)*(3 - x))/x)])/20 + (E^x*x^2*Log[-(((E^x - 5*x)*(3 - x))
/x)])/2 - (E^(2*x)*x^2*Log[-(((E^x - 5*x)*(3 - x))/x)])/10 - (5*x^3*Log[-(((E^x - 5*x)*(3 - x))/x)])/6 + (5*x^
4*Log[-(((E^x - 5*x)*(3 - x))/x)])/8 + (3*E^6*ExpIntegralEi[-2*(3 - x)]*Log[-(((E^x - 5*x)*(3 - x))/x)])/10 +
(15*Defer[Int][E^x/(E^x - 5*x), x])/2 - 15*Defer[Int][(E^x*x)/(E^x - 5*x), x] - (25*Defer[Int][x^2/(E^x - 5*x)
, x])/8 + 10*Defer[Int][(E^x*x^2)/(E^x - 5*x), x] + (125*Defer[Int][x^3/(E^x - 5*x), x])/24 - (25*Log[-(((E^x
- 5*x)*(3 - x))/x)]*Defer[Int][x^3/(E^x - 5*x), x])/2 - (5*Defer[Int][(E^x*x^3)/(E^x - 5*x), x])/2 + (25*Defer
[Int][x^4/(E^x - 5*x), x])/24 + (25*Log[-(((E^x - 5*x)*(3 - x))/x)]*Defer[Int][x^4/(E^x - 5*x), x])/2 - (25*De
fer[Int][x^5/(E^x - 5*x), x])/8 + (3*E^6*Defer[Int][ExpIntegralEi[-6 + 2*x]/(E^x - 5*x), x])/2 - (3*E^6*Defer[
Int][ExpIntegralEi[-6 + 2*x]/(-3 + x), x])/10 + (3*E^6*Defer[Int][ExpIntegralEi[-6 + 2*x]/x, x])/10 - (3*E^6*D
efer[Int][(x*ExpIntegralEi[-6 + 2*x])/(E^x - 5*x), x])/2 + Defer[Int][E^(2*x)*Log[((E^x - 5*x)*(-3 + x))/x]^2,
x]/20 + Defer[Int][E^(2*x)*x*Log[((E^x - 5*x)*(-3 + x))/x]^2, x]/10 + (25*Defer[Int][Defer[Int][x^3/(E^x - 5*
x), x], x])/2 - (125*Defer[Int][Defer[Int][x^3/(E^x - 5*x), x]/(E^x - 5*x), x])/2 + (25*Defer[Int][Defer[Int][
x^3/(E^x - 5*x), x]/(-3 + x), x])/2 - (25*Defer[Int][Defer[Int][x^3/(E^x - 5*x), x]/x, x])/2 + (125*Defer[Int]
[(x*Defer[Int][x^3/(E^x - 5*x), x])/(E^x - 5*x), x])/2 - (25*Defer[Int][Defer[Int][x^4/(E^x - 5*x), x], x])/2
+ (125*Defer[Int][Defer[Int][x^4/(E^x - 5*x), x]/(E^x - 5*x), x])/2 - (25*Defer[Int][Defer[Int][x^4/(E^x - 5*x
), x]/(-3 + x), x])/2 + (25*Defer[Int][Defer[Int][x^4/(E^x - 5*x), x]/x, x])/2 - (125*Defer[Int][(x*Defer[Int]
[x^4/(E^x - 5*x), x])/(E^x - 5*x), x])/2

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{-300x+100x^2-e^x(-60+20x)-e^{3x}(-6x-3x^2-5x^3+2x^4)-e^{2x}(55x^3+15x^4-10x^5)-(e^{3x}(6+6x+10x^2-4x^3)+e^{2x}(-70x^2-40x^3+20x^4))\log \left(\frac{e^x(-3+x)+15x-5x^2}{x}\right)-(e^{3x}(-3-5x+2x^2)+e^{2x}(15x+25x^2-10x^3)){\log }^2\left(\frac{e^x(-3+x)+15x-5x^2}{x}\right)}{20(e^x-5x)(3-x)}dx\\ & =\frac{1}{20}\int \frac{-300x+100x^2-e^x(-60+20x)-e^{3x}(-6x-3x^2-5x^3+2x^4)-e^{2x}(55x^3+15x^4-10x^5)-(e^{3x}(6+6x+10x^2-4x^3)+e^{2x}(-70x^2-40x^3+20x^4))\log \left(\frac{e^x(-3+x)+15x-5x^2}{x}\right)-(e^{3x}(-3-5x+2x^2)+e^{2x}(15x+25x^2-10x^3)){\log }^2\left(\frac{e^x(-3+x)+15x-5x^2}{x}\right)}{(e^x-5x)(3-x)}dx\\ & =\frac{1}{20}\int (-10e^x(-1+x)x(x-\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))-\frac{250(-1+x)x^3(x-\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))}{e^x-5x}-10(-2-5x^3+5x^4+5x^2\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)-5x^3\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))+\frac{e^{2x}(-6x-3x^2-5x^3+2x^4+6\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)+6x\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)+10x^2\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)-4x^3\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)-3{\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right)-5x{\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right)+2x^2{\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right))}{-3+x})dx\\ & =\frac{1}{20}\int \frac{e^{2x}(-6x-3x^2-5x^3+2x^4+6\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)+6x\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)+10x^2\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)-4x^3\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)-3{\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right)-5x{\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right)+2x^2{\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right))}{-3+x}dx-\frac{1}{2}\int e^x(-1+x)x(x-\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))dx-\frac{1}{2}\int (-2-5x^3+5x^4+5x^2\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)-5x^3\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))dx-\frac{25}{2}\int \frac{(-1+x)x^3(x-\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))}{e^x-5x}dx\\ & =x+\frac{5x^4}{8}-\frac{x^5}{2}+\frac{1}{20}\int \frac{e^{2x}(-x(-6-3x-5x^2+2x^3)-(6+6x+10x^2-4x^3)\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)-(-3-5x+2x^2){\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right))}{3-x}dx-\frac{1}{2}\int (e^x(-1+x)x^2-e^x(-1+x)x\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))dx-\frac{5}{2}\int x^2\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)dx+\frac{5}{2}\int x^3\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)dx-\frac{25}{2}\int (-\frac{x^3(x-\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))}{e^x-5x}+\frac{x^4(x-\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))}{e^x-5x})dx\\ & =x+\frac{5x^4}{8}-\frac{x^5}{2}-\frac{5}{6}{x}^3\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{5}{8}{x}^4\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{1}{20}\int (\frac{e^{2x}x(-6-3x-5x^2+2x^3)}{-3+x}-\frac{2e^{2x}(-3-3x-5x^2+2x^3)\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)}{-3+x}+e^{2x}(1+2x){\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right))dx-\frac{1}{2}\int e^x(-1+x)x^{2}dx+\frac{1}{2}\int e^x(-1+x)x\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)dx-\frac{5}{8}\int \frac{5x^5-e^x{x}^3(3-3x+x^2)}{(e^x-5x)(3-x)}dx+\frac{5}{6}\int \frac{5x^4-e^x{x}^2(3-3x+x^2)}{(e^x-5x)(3-x)}dx+\frac{25}{2}\int \frac{x^3(x-\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))}{e^x-5x}dx-\frac{25}{2}\int \frac{x^4(x-\log \left(\frac{(e^x-5x)(-3+x)}{x}\right))}{e^x-5x}dx\\ & =x+\frac{5x^4}{8}-\frac{x^5}{2}+\frac{3}{2}{e}^x\log (-\frac{(e^x-5x)(3-x)}{x})-\frac{3}{2}{e}^{x}x\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{1}{2}{e}^x{x}^2\log (-\frac{(e^x-5x)(3-x)}{x})-\frac{5}{6}{x}^3\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{5}{8}{x}^4\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{1}{20}\int \frac{e^{2x}x(-6-3x-5x^2+2x^3)}{-3+x}dx+\frac{1}{20}\int e^{2x}(1+2x){\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right)dx-\frac{1}{10}\int \frac{e^{2x}(-3-3x-5x^2+2x^3)\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)}{-3+x}dx-\frac{1}{2}\int (-e^x{x}^2+e^x{x}^3)dx-\frac{1}{2}\int \frac{e^x(3-3x+x^2)(5x^2-e^x(3-3x+x^2))}{(e^x-5x)(3-x)x}dx-\frac{5}{8}\int (\frac{5(-1+x)x^4}{e^x-5x}+\frac{x^3(3-3x+x^2)}{-3+x})dx+\frac{5}{6}\int (\frac{5(-1+x)x^3}{e^x-5x}+\frac{x^2(3-3x+x^2)}{-3+x})dx+\frac{25}{2}\int (\frac{x^4}{e^x-5x}-\frac{x^3\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)}{e^x-5x})dx-\frac{25}{2}\int (\frac{x^5}{e^x-5x}-\frac{x^4\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)}{e^x-5x})dx\\ & =x+\frac{5x^4}{8}-\frac{x^5}{2}+\frac{3}{2}{e}^x\log (-\frac{(e^x-5x)(3-x)}{x})-\frac{1}{40}{e}^{2x}\log (-\frac{(e^x-5x)(3-x)}{x})-\frac{3}{2}{e}^{x}x\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{1}{20}{e}^{2x}x\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{1}{2}{e}^x{x}^2\log (-\frac{(e^x-5x)(3-x)}{x})-\frac{1}{10}{e}^{2x}{x}^2\log (-\frac{(e^x-5x)(3-x)}{x})-\frac{5}{6}{x}^3\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{5}{8}{x}^4\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{3}{10}{e}^6\text{Ei}(-2(3-x))\log (-\frac{(e^x-5x)(3-x)}{x})+\frac{1}{20}\int (-6e^{2x}-\frac{18e^{2x}}{-3+x}+e^{2x}{x}^2+2e^{2x}{x}^3)dx+\frac{1}{20}\int (e^{2x}{\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right)+2e^{2x}x{\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right))dx+\frac{1}{10}\int \frac{(5x^2-e^x(3-3x+x^2))(e^{2x}(1-2x+4x^2)-12e^6\text{Ei}(-6+2x))}{4(e^x-5x)(3-x)x}dx+\frac{1}{2}\int e^x{x}^{2}dx-\frac{1}{2}\int e^x{x}^{3}dx-\frac{1}{2}\int (\frac{e^x{(3-3x+x^2)}^2}{(-3+x)x}+\frac{5e^x(-3+6x-4x^2+x^3)}{e^x-5x})dx-\frac{5}{8}\int \frac{x^3(3-3x+x^2)}{-3+x}dx+\frac{5}{6}\int \frac{x^2(3-3x+x^2)}{-3+x}dx-\frac{25}{8}\int \frac{(-1+x)x^4}{e^x-5x}dx+\frac{25}{6}\int \frac{(-1+x)x^3}{e^x-5x}dx+\frac{25}{2}\int \frac{x^4}{e^x-5x}dx-\frac{25}{2}\int \frac{x^5}{e^x-5x}dx-\frac{25}{2}\int \frac{x^3\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)}{e^x-5x}dx+\frac{25}{2}\int \frac{x^4\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)}{e^x-5x}dx\\ & =\text{Rest of rules removed due to large latex content}\end{array}\end{array}$$

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Mathematica [A]  time = 0.12, size = 62, normalized size = 1.68 $$\begin{array}{c}\frac{1}{20}x(20+e^{2x}{x}^2-2e^{2x}x\log \left(\frac{(e^x-5x)(-3+x)}{x}\right)+e^{2x}{\log }^2\left(\frac{(e^x-5x)(-3+x)}{x}\right))\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(300*x - 100*x^2 + E^x*(-60 + 20*x) + E^(3*x)*(-6*x - 3*x^2 - 5*x^3 + 2*x^4) + E^(2*x)*(55*x^3 + 15*
x^4 - 10*x^5) + (E^(3*x)*(6 + 6*x + 10*x^2 - 4*x^3) + E^(2*x)*(-70*x^2 - 40*x^3 + 20*x^4))*Log[(E^x*(-3 + x) +
15*x - 5*x^2)/x] + (E^(3*x)*(-3 - 5*x + 2*x^2) + E^(2*x)*(15*x + 25*x^2 - 10*x^3))*Log[(E^x*(-3 + x) + 15*x -
5*x^2)/x]^2)/(300*x - 100*x^2 + E^x*(-60 + 20*x)),x]

[Out]

(x*(20 + E^(2*x)*x^2 - 2*E^(2*x)*x*Log[((E^x - 5*x)*(-3 + x))/x] + E^(2*x)*Log[((E^x - 5*x)*(-3 + x))/x]^2))/2
0

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fricas [B]  time = 0.88, size = 73, normalized size = 1.97 $$\begin{array}{c}\frac{1}{20}{x}^3{e}^{\left(2x\right)}-\frac{1}{10}{x}^2{e}^{\left(2x\right)}\log (-\frac{5x^2-(x-3)e^x-15x}{x})+\frac{1}{20}x{e}^{\left(2x\right)}\log {(-\frac{5x^2-(x-3)e^x-15x}{x})}^2+x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*log(((x-3)*exp(x)-5*x^2+15*x)/x)^2+((-4*x^3
+10*x^2+6*x+6)*exp(x)^3+(20*x^4-40*x^3-70*x^2)*exp(x)^2)*log(((x-3)*exp(x)-5*x^2+15*x)/x)+(2*x^4-5*x^3-3*x^2-6
*x)*exp(x)^3+(-10*x^5+15*x^4+55*x^3)*exp(x)^2+(20*x-60)*exp(x)-100*x^2+300*x)/((20*x-60)*exp(x)-100*x^2+300*x)
,x, algorithm="fricas")

[Out]

1/20*x^3*e^(2*x) - 1/10*x^2*e^(2*x)*log(-(5*x^2 - (x - 3)*e^x - 15*x)/x) + 1/20*x*e^(2*x)*log(-(5*x^2 - (x - 3
)*e^x - 15*x)/x)^2 + x

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giac [B]  time = 1.18, size = 77, normalized size = 2.08 $$\begin{array}{c}\frac{1}{20}{x}^3{e}^{\left(2x\right)}-\frac{1}{10}{x}^2{e}^{\left(2x\right)}\log (-\frac{5x^2-x{e}^x-15x+3e^x}{x})+\frac{1}{20}x{e}^{\left(2x\right)}\log {(-\frac{5x^2-x{e}^x-15x+3e^x}{x})}^2+x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*log(((x-3)*exp(x)-5*x^2+15*x)/x)^2+((-4*x^3
+10*x^2+6*x+6)*exp(x)^3+(20*x^4-40*x^3-70*x^2)*exp(x)^2)*log(((x-3)*exp(x)-5*x^2+15*x)/x)+(2*x^4-5*x^3-3*x^2-6
*x)*exp(x)^3+(-10*x^5+15*x^4+55*x^3)*exp(x)^2+(20*x-60)*exp(x)-100*x^2+300*x)/((20*x-60)*exp(x)-100*x^2+300*x)
,x, algorithm="giac")

[Out]

1/20*x^3*e^(2*x) - 1/10*x^2*e^(2*x)*log(-(5*x^2 - x*e^x - 15*x + 3*e^x)/x) + 1/20*x*e^(2*x)*log(-(5*x^2 - x*e^
x - 15*x + 3*e^x)/x)^2 + x

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maple [C]  time = 0.40, size = 2157, normalized size = 58.30

method	result	size
risch	$\text{Expression too large to display}$	$2157$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*ln(((x-3)*exp(x)-5*x^2+15*x)/x)^2+((-4*x^3+10*x^2
+6*x+6)*exp(x)^3+(20*x^4-40*x^3-70*x^2)*exp(x)^2)*ln(((x-3)*exp(x)-5*x^2+15*x)/x)+(2*x^4-5*x^3-3*x^2-6*x)*exp(
x)^3+(-10*x^5+15*x^4+55*x^3)*exp(x)^2+(20*x-60)*exp(x)-100*x^2+300*x)/((20*x-60)*exp(x)-100*x^2+300*x),x,metho
d=_RETURNVERBOSE)

[Out]

x+1/20*exp(2*x)*x^3-1/20*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^5*exp(2*x)+1/10*Pi^2*x*csgn(I*(-
x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/10*I*Pi*x^2*exp(2*x)-1/80*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3
)*x-3/5*exp(x))/x)^6*exp(2*x)-1/10*ln(5)*x*exp(2*x)*ln(x)+1/20*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x
))/x)^3*exp(2*x)-1/20*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^4*exp(2*x)+1/20*I*Pi*x*csgn(I*(-x^2
-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)*ln(x)+1/20*I*Pi*ln(5)
*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/20*I*Pi*x*csgn(I/x)*csgn(I*(-x^2-(-1/5
*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)*ln(x)+1/20*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/
x)^4*exp(2*x)+1/20*I*Pi*x^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp(2*x)-1/80*Pi^2*x*csgn(I*(-x^2-
(-1/5*exp(x)-3)*x-3/5*exp(x)))^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^4*exp(2*x)+(-1/10*x*exp(2*x)*ln
(x)-1/20*I*Pi*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x
))/x)*exp(2*x)+1/20*I*Pi*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/10*I*Pi*x*csgn
(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/20*I*Pi*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*c
sgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/20*I*Pi*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))
/x)^3*exp(2*x)+1/10*I*Pi*x*exp(2*x)+1/10*x*ln(5)*exp(2*x)-1/10*exp(2*x)*x^2)*ln(x^2+(-1/5*exp(x)-3)*x+3/5*exp(
x))-1/10*I*Pi*x*exp(2*x)*ln(x)-1/20*Pi^2*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(
x)-3)*x-3/5*exp(x))/x)^4*exp(2*x)-1/20*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x
^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp(2*x)+1/20*I*Pi*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp
(2*x)*ln(x)-1/20*I*Pi*ln(5)*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp(2*x)+1/20*Pi^2*x*csgn(I/x)*c
sgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)*exp(2*x)-1/80*Pi^2*x*
csgn(I/x)^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(
2*x)+1/20*x*exp(2*x)*ln(x^2+(-1/5*exp(x)-3)*x+3/5*exp(x))^2-1/20*Pi^2*x*exp(2*x)+1/20*ln(5)^2*x*exp(2*x)+1/20*
x*exp(2*x)*ln(x)^2+1/10*x^2*exp(2*x)*ln(x)-1/10*x^2*ln(5)*exp(2*x)+1/10*I*Pi*ln(5)*x*exp(2*x)-1/40*Pi^2*x*csgn
(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^5*exp(2*x)+1/20*Pi^2*x*c
sgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)+1/10*I*Pi*
x^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/20*I*Pi*x^2*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)
-3)*x-3/5*exp(x))/x)^2*exp(2*x)-1/40*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))^2*csgn(I*(-x
^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^3*exp(2*x)-1/20*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)
)/x)^2*exp(2*x)-1/80*Pi^2*x*csgn(I/x)^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^4*exp(2*x)+1/20*I*Pi*x*c
sgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)*exp(2*x)*ln
(x)-1/20*I*Pi*ln(5)*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5
*exp(x))/x)*exp(2*x)+1/40*Pi^2*x*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^5*exp(2*x)+1/20*I*Pi*
x^2*csgn(I/x)*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)*exp(2*
x)-1/20*I*Pi*ln(5)*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)
^2*exp(2*x)+1/40*Pi^2*x*csgn(I/x)^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)-3)*x
-3/5*exp(x))/x)^3*exp(2*x)+1/20*I*Pi*x^2*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x)))*csgn(I*(-x^2-(-1/5*exp(x)
-3)*x-3/5*exp(x))/x)^2*exp(2*x)+1/10*I*Pi*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)*ln(x)-1/1
0*I*Pi*ln(5)*x*csgn(I*(-x^2-(-1/5*exp(x)-3)*x-3/5*exp(x))/x)^2*exp(2*x)

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maxima [B]  time = 0.75, size = 106, normalized size = 2.86 $$\begin{array}{c}\frac{1}{20}x{e}^{\left(2x\right)}\log {(x-3)}^2+\frac{1}{20}x{e}^{\left(2x\right)}\log {(-5x+e^x)}^2-\frac{1}{10}(x^2+x\log (x))e^{\left(2x\right)}\log (x-3)+\frac{1}{20}(x^3+2x^2\log (x)+x\log (x{)}^2)e^{\left(2x\right)}+\frac{1}{10}(x{e}^{\left(2x\right)}\log (x-3)-(x^2+x\log (x))e^{\left(2x\right)})\log (-5x+e^x)+x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x^2-5*x-3)*exp(x)^3+(-10*x^3+25*x^2+15*x)*exp(x)^2)*log(((x-3)*exp(x)-5*x^2+15*x)/x)^2+((-4*x^3
+10*x^2+6*x+6)*exp(x)^3+(20*x^4-40*x^3-70*x^2)*exp(x)^2)*log(((x-3)*exp(x)-5*x^2+15*x)/x)+(2*x^4-5*x^3-3*x^2-6
*x)*exp(x)^3+(-10*x^5+15*x^4+55*x^3)*exp(x)^2+(20*x-60)*exp(x)-100*x^2+300*x)/((20*x-60)*exp(x)-100*x^2+300*x)
,x, algorithm="maxima")

[Out]

1/20*x*e^(2*x)*log(x - 3)^2 + 1/20*x*e^(2*x)*log(-5*x + e^x)^2 - 1/10*(x^2 + x*log(x))*e^(2*x)*log(x - 3) + 1/
20*(x^3 + 2*x^2*log(x) + x*log(x)^2)*e^(2*x) + 1/10*(x*e^(2*x)*log(x - 3) - (x^2 + x*log(x))*e^(2*x))*log(-5*x
+ e^x) + x

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mupad [B]  time = 4.45, size = 69, normalized size = 1.86 $$\begin{array}{c}x+\frac{x^3{\mathrm{e}}^{2x}}{20}+\frac{x{\ln \left(\frac{15x+{\mathrm{e}}^x(x-3)-5x^2}{x}\right)}^2{\mathrm{e}}^{2x}}{20}-\frac{x^2\ln \left(\frac{15x+{\mathrm{e}}^x(x-3)-5x^2}{x}\right){\mathrm{e}}^{2x}}{10}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((300*x + exp(x)*(20*x - 60) - exp(3*x)*(6*x + 3*x^2 + 5*x^3 - 2*x^4) - log((15*x + exp(x)*(x - 3) - 5*x^2)
/x)^2*(exp(3*x)*(5*x - 2*x^2 + 3) - exp(2*x)*(15*x + 25*x^2 - 10*x^3)) + exp(2*x)*(55*x^3 + 15*x^4 - 10*x^5) +
log((15*x + exp(x)*(x - 3) - 5*x^2)/x)*(exp(3*x)*(6*x + 10*x^2 - 4*x^3 + 6) - exp(2*x)*(70*x^2 + 40*x^3 - 20*
x^4)) - 100*x^2)/(300*x + exp(x)*(20*x - 60) - 100*x^2),x)

[Out]

x + (x^3*exp(2*x))/20 + (x*log((15*x + exp(x)*(x - 3) - 5*x^2)/x)^2*exp(2*x))/20 - (x^2*log((15*x + exp(x)*(x
- 3) - 5*x^2)/x)*exp(2*x))/10

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sympy [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\text{Exception raised: ShapeError}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x**2-5*x-3)*exp(x)**3+(-10*x**3+25*x**2+15*x)*exp(x)**2)*ln(((x-3)*exp(x)-5*x**2+15*x)/x)**2+((
-4*x**3+10*x**2+6*x+6)*exp(x)**3+(20*x**4-40*x**3-70*x**2)*exp(x)**2)*ln(((x-3)*exp(x)-5*x**2+15*x)/x)+(2*x**4
-5*x**3-3*x**2-6*x)*exp(x)**3+(-10*x**5+15*x**4+55*x**3)*exp(x)**2+(20*x-60)*exp(x)-100*x**2+300*x)/((20*x-60)
*exp(x)-100*x**2+300*x),x)

[Out]

Exception raised: ShapeError

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