3.69.85 $\int \frac{x^{-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(2100-200x-25x^2+(200x+50x^2)\log (x)+e^{-4-2x+2x^2}{x}^2(-25+(50-50x+100x^2)\log (x))+e^{-2-x+x^2}x(-200-50x+(200-100x+350x^2+100x^3)\log (x)))}{7056x-1344x^2-104x^3+16x^4+x^5+e^{-8-4x+4x^2}{x}^5+e^{-6-3x+3x^2}{x}^3(16x+4x^2)+e^{-4-2x+2x^2}{x}^2(-104x+48x^2+6x^3)+e^{-2-x+x^2}x(-1344x-208x^2+48x^3+4x^4)}dx$

Optimal. Leaf size=27 $$x^{\frac{1}{4-\frac{1}{25}{(4+x+e^{-2-x+x^2}x)}^2}}$$

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Rubi [F]  time = 66.06, 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 = {} $$\begin{array}{c}\int \frac{x^{-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(2100-200x-25x^2+(200x+50x^2)\log (x)+e^{-4-2x+2x^2}{x}^2(-25+(50-50x+100x^2)\log (x))+e^{-2-x+x^2}x(-200-50x+(200-100x+350x^2+100x^3)\log (x)))}{7056x-1344x^2-104x^3+16x^4+x^5+e^{-8-4x+4x^2}{x}^5+e^{-6-3x+3x^2}{x}^3(16x+4x^2)+e^{-4-2x+2x^2}{x}^2(-104x+48x^2+6x^3)+e^{-2-x+x^2}x(-1344x-208x^2+48x^3+4x^4)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(2100 - 200*x - 25*x^2 + (200*x + 50*x^2)*Log[x] + E^(-4 - 2*x + 2*x^2)*x^2*(-25 + (50 - 50*x + 100*x^2)*L
og[x]) + E^(-2 - x + x^2)*x*(-200 - 50*x + (200 - 100*x + 350*x^2 + 100*x^3)*Log[x]))/(x^(25/(-84 + 8*x + x^2
+ E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(7056*x - 1344*x^2 - 104*x^3 + 16*x^4 + x^5 + E^(-
8 - 4*x + 4*x^2)*x^5 + E^(-6 - 3*x + 3*x^2)*x^3*(16*x + 4*x^2) + E^(-4 - 2*x + 2*x^2)*x^2*(-104*x + 48*x^2 + 6
*x^3) + E^(-2 - x + x^2)*x*(-1344*x - 208*x^2 + 48*x^3 + 4*x^4))),x]

[Out]

(-15*Log[x]*Defer[Int][E^(4 + 2*x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8
+ 2*x)))*(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2), x])/2 + (15*Log[x]*Defer[Int][(E^(4 + 2*x)*x^(-1 - 25/(-84
+ 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*
x)^2, x])/2 + (65*Log[x]*Defer[Int][(E^(4 + 2*x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2
- x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2, x])/4 - (5*Log[x]*Defer[Int][(E^(4 + 2*x)
*x^(2 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2
*x + E^(2 + x)*x)^2, x])/2 - (5*Log[x]*Defer[Int][E^(2 + x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2
+ E^(-2 - x + x^2)*x*(8 + 2*x)))*(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*x)), x])/4 - (5*Defer[Int][(E^(2 + x)*x^
(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2*x
+ E^(2 + x)*x), x])/4 + (5*Log[x]*Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^
2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) + E^x^2*x + E^(2 + x)*x), x])/4 + (5*Log[x]*Defer[Int][(E^(2
+ x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(-6*E^(2 + x) +
E^x^2*x + E^(2 + x)*x), x])/2 - (35*Log[x]*Defer[Int][E^(4 + 2*x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^
2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2), x])/2 + (35*Log[x]*Defer[In
t][(E^(4 + 2*x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(14*E
^(2 + x) + E^x^2*x + E^(2 + x)*x)^2, x])/2 + (135*Log[x]*Defer[Int][(E^(4 + 2*x)*x^(1 - 25/(-84 + 8*x + x^2 +
E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2, x])/4 + (
5*Log[x]*Defer[Int][(E^(4 + 2*x)*x^(2 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8
+ 2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x)^2, x])/2 + (5*Log[x]*Defer[Int][E^(2 + x)/(x^(25/(-84 + 8*x
+ x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x)), x])
/4 + (5*Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 +
2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x), x])/4 - (5*Log[x]*Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x
+ x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x), x]
)/4 - (5*Log[x]*Defer[Int][(E^(2 + x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)
*x*(8 + 2*x))))/(14*E^(2 + x) + E^x^2*x + E^(2 + x)*x), x])/2 + (15*Defer[Int][Defer[Int][E^(4 + 2*x)/(x^(25/(
-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x)))*(E^(2 + x)*(-6 + x) + E^x^2*x)^2),
x]/x, x])/2 - (15*Defer[Int][Defer[Int][(E^(4 + 2*x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 +
2*E^(-2 - x + x^2)*x*(4 + x))))/(E^(2 + x)*(-6 + x) + E^x^2*x)^2, x]/x, x])/2 - (65*Defer[Int][Defer[Int][(E^
(4 + 2*x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^(2 + x)*(
-6 + x) + E^x^2*x)^2, x]/x, x])/4 + (5*Defer[Int][Defer[Int][(E^(4 + 2*x)*x^(2 - 25/(-84 + 8*x + x^2 + E^(-4 -
2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^(2 + x)*(-6 + x) + E^x^2*x)^2, x]/x, x])/2 + (5*Defer[I
nt][Defer[Int][E^(2 + x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x)))*(
E^(2 + x)*(-6 + x) + E^x^2*x)), x]/x, x])/4 - (5*Defer[Int][Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x + x^2
+ E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^(2 + x)*(-6 + x) + E^x^2*x), x]/x, x])/4 - (5*
Defer[Int][Defer[Int][(E^(2 + x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*
(4 + x))))/(E^(2 + x)*(-6 + x) + E^x^2*x), x]/x, x])/2 + (35*Defer[Int][Defer[Int][E^(4 + 2*x)/(x^(25/(-84 + 8
*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x)))*(E^x^2*x + E^(2 + x)*(14 + x))^2), x]/x,
x])/2 - (35*Defer[Int][Defer[Int][(E^(4 + 2*x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-
2 - x + x^2)*x*(4 + x))))/(E^x^2*x + E^(2 + x)*(14 + x))^2, x]/x, x])/2 - (135*Defer[Int][Defer[Int][(E^(4 + 2
*x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^x^2*x + E^(2 +
x)*(14 + x))^2, x]/x, x])/4 - (5*Defer[Int][Defer[Int][(E^(4 + 2*x)*x^(2 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x +
2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^x^2*x + E^(2 + x)*(14 + x))^2, x]/x, x])/2 - (5*Defer[Int][De
fer[Int][E^(2 + x)/(x^(25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x)))*(E^x^2*
x + E^(2 + x)*(14 + x))), x]/x, x])/4 + (5*Defer[Int][Defer[Int][(E^(2 + x)*x^(-1 - 25/(-84 + 8*x + x^2 + E^(-
4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x))))/(E^x^2*x + E^(2 + x)*(14 + x)), x]/x, x])/4 + (5*Defer[
Int][Defer[Int][(E^(2 + x)*x^(1 - 25/(-84 + 8*x + x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + 2*E^(-2 - x + x^2)*x*(4 + x
))))/(E^x^2*x + E^(2 + x)*(14 + x)), x]/x, x])/2

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e^{8+4x}{x}^{-1-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(2100-200x-25x^2+(200x+50x^2)\log (x)+e^{-4-2x+2x^2}{x}^2(-25+(50-50x+100x^2)\log (x))+e^{-2-x+x^2}x(-200-50x+(200-100x+350x^2+100x^3)\log (x)))}{{(84e^{4+2x}-8e^{4+2x}x-8e^{2+x+x^2}x-e^{2x^2}{x}^2-e^{4+2x}{x}^2-2e^{2+x+x^2}{x}^2)}^2}dx\\ & =\int (-\frac{5e^{4+2x}{x}^{-1-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(-6+6x-13x^2+2x^3)\log (x)}{4{(-6e^{2+x}+e^{x^2}x+e^{2+x}x)}^2}+\frac{5e^{4+2x}{x}^{-1-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(14-14x+27x^2+2x^3)\log (x)}{4{(14e^{2+x}+e^{x^2}x+e^{2+x}x)}^2}+\frac{5e^{2+x}{x}^{-1-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(-1+\log (x)-x\log (x)+2x^2\log (x))}{4(-6e^{2+x}+e^{x^2}x+e^{2+x}x)}-\frac{5e^{2+x}{x}^{-1-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(-1+\log (x)-x\log (x)+2x^2\log (x))}{4(14e^{2+x}+e^{x^2}x+e^{2+x}x)})dx\\ & =-(\frac{5}{4}\int \frac{e^{4+2x}{x}^{-1-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(-6+6x-13x^2+2x^3)\log (x)}{{(-6e^{2+x}+e^{x^2}x+e^{2+x}x)}^2}dx)+\frac{5}{4}\int \frac{e^{4+2x}{x}^{-1-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(14-14x+27x^2+2x^3)\log (x)}{{(14e^{2+x}+e^{x^2}x+e^{2+x}x)}^2}dx+\frac{5}{4}\int \frac{e^{2+x}{x}^{-1-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(-1+\log (x)-x\log (x)+2x^2\log (x))}{-6e^{2+x}+e^{x^2}x+e^{2+x}x}dx-\frac{5}{4}\int \frac{e^{2+x}{x}^{-1-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(-1+\log (x)-x\log (x)+2x^2\log (x))}{14e^{2+x}+e^{x^2}x+e^{2+x}x}dx\\ & =\text{Rest of rules removed due to large latex content}\end{array}\end{array}$$

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Mathematica [F]  time = 2.19, size = 0, normalized size = 0.00 $$\begin{array}{c}\int \frac{x^{-\frac{25}{-84+8x+x^2+e^{-4-2x+2x^2}{x}^2+e^{-2-x+x^2}x(8+2x)}}(2100-200x-25x^2+(200x+50x^2)\log (x)+e^{-4-2x+2x^2}{x}^2(-25+(50-50x+100x^2)\log (x))+e^{-2-x+x^2}x(-200-50x+(200-100x+350x^2+100x^3)\log (x)))}{7056x-1344x^2-104x^3+16x^4+x^5+e^{-8-4x+4x^2}{x}^5+e^{-6-3x+3x^2}{x}^3(16x+4x^2)+e^{-4-2x+2x^2}{x}^2(-104x+48x^2+6x^3)+e^{-2-x+x^2}x(-1344x-208x^2+48x^3+4x^4)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Integrate[(2100 - 200*x - 25*x^2 + (200*x + 50*x^2)*Log[x] + E^(-4 - 2*x + 2*x^2)*x^2*(-25 + (50 - 50*x + 100*
x^2)*Log[x]) + E^(-2 - x + x^2)*x*(-200 - 50*x + (200 - 100*x + 350*x^2 + 100*x^3)*Log[x]))/(x^(25/(-84 + 8*x
+ x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(7056*x - 1344*x^2 - 104*x^3 + 16*x^4 + x^5
+ E^(-8 - 4*x + 4*x^2)*x^5 + E^(-6 - 3*x + 3*x^2)*x^3*(16*x + 4*x^2) + E^(-4 - 2*x + 2*x^2)*x^2*(-104*x + 48*x
^2 + 6*x^3) + E^(-2 - x + x^2)*x*(-1344*x - 208*x^2 + 48*x^3 + 4*x^4))),x]

[Out]

Integrate[(2100 - 200*x - 25*x^2 + (200*x + 50*x^2)*Log[x] + E^(-4 - 2*x + 2*x^2)*x^2*(-25 + (50 - 50*x + 100*
x^2)*Log[x]) + E^(-2 - x + x^2)*x*(-200 - 50*x + (200 - 100*x + 350*x^2 + 100*x^3)*Log[x]))/(x^(25/(-84 + 8*x
+ x^2 + E^(-4 - 2*x + 2*x^2)*x^2 + E^(-2 - x + x^2)*x*(8 + 2*x)))*(7056*x - 1344*x^2 - 104*x^3 + 16*x^4 + x^5
+ E^(-8 - 4*x + 4*x^2)*x^5 + E^(-6 - 3*x + 3*x^2)*x^3*(16*x + 4*x^2) + E^(-4 - 2*x + 2*x^2)*x^2*(-104*x + 48*x
^2 + 6*x^3) + E^(-2 - x + x^2)*x*(-1344*x - 208*x^2 + 48*x^3 + 4*x^4))), x]

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fricas [A]  time = 3.18, size = 47, normalized size = 1.74 $$\begin{array}{c}\frac{1}{x^{\frac{25}{x^2+2(x+4)e^{(x^2-x+\log (x)-2)}+8x+e^{(2x^2-2x+2\log (x)-4)}-84}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((100*x^2-50*x+50)*log(x)-25)*exp(log(x)+x^2-x-2)^2+((100*x^3+350*x^2-100*x+200)*log(x)-50*x-200)*e
xp(log(x)+x^2-x-2)+(50*x^2+200*x)*log(x)-25*x^2-200*x+2100)*exp(-25*log(x)/(exp(log(x)+x^2-x-2)^2+(2*x+8)*exp(
log(x)+x^2-x-2)+x^2+8*x-84))/(x*exp(log(x)+x^2-x-2)^4+(4*x^2+16*x)*exp(log(x)+x^2-x-2)^3+(6*x^3+48*x^2-104*x)*
exp(log(x)+x^2-x-2)^2+(4*x^4+48*x^3-208*x^2-1344*x)*exp(log(x)+x^2-x-2)+x^5+16*x^4-104*x^3-1344*x^2+7056*x),x,
algorithm="fricas")

[Out]

1/(x^(25/(x^2 + 2*(x + 4)*e^(x^2 - x + log(x) - 2) + 8*x + e^(2*x^2 - 2*x + 2*log(x) - 4) - 84)))

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\text{Timed out}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((100*x^2-50*x+50)*log(x)-25)*exp(log(x)+x^2-x-2)^2+((100*x^3+350*x^2-100*x+200)*log(x)-50*x-200)*e
xp(log(x)+x^2-x-2)+(50*x^2+200*x)*log(x)-25*x^2-200*x+2100)*exp(-25*log(x)/(exp(log(x)+x^2-x-2)^2+(2*x+8)*exp(
log(x)+x^2-x-2)+x^2+8*x-84))/(x*exp(log(x)+x^2-x-2)^4+(4*x^2+16*x)*exp(log(x)+x^2-x-2)^3+(6*x^3+48*x^2-104*x)*
exp(log(x)+x^2-x-2)^2+(4*x^4+48*x^3-208*x^2-1344*x)*exp(log(x)+x^2-x-2)+x^5+16*x^4-104*x^3-1344*x^2+7056*x),x,
algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.06, size = 52, normalized size = 1.93

method	result	size
risch	$x^{-\frac{25}{x^2{\mathrm{e}}^{2(x+1)(x-2)}+2x^2{\mathrm{e}}^{(x+1)(x-2)}+8x{\mathrm{e}}^{(x+1)(x-2)}+x^2+8x-84}}$	$52$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((100*x^2-50*x+50)*ln(x)-25)*exp(ln(x)+x^2-x-2)^2+((100*x^3+350*x^2-100*x+200)*ln(x)-50*x-200)*exp(ln(x)+
x^2-x-2)+(50*x^2+200*x)*ln(x)-25*x^2-200*x+2100)*exp(-25*ln(x)/(exp(ln(x)+x^2-x-2)^2+(2*x+8)*exp(ln(x)+x^2-x-2
)+x^2+8*x-84))/(x*exp(ln(x)+x^2-x-2)^4+(4*x^2+16*x)*exp(ln(x)+x^2-x-2)^3+(6*x^3+48*x^2-104*x)*exp(ln(x)+x^2-x-
2)^2+(4*x^4+48*x^3-208*x^2-1344*x)*exp(ln(x)+x^2-x-2)+x^5+16*x^4-104*x^3-1344*x^2+7056*x),x,method=_RETURNVERB
OSE)

[Out]

x^(-25/(x^2*exp(2*(x+1)*(x-2))+2*x^2*exp((x+1)*(x-2))+8*x*exp((x+1)*(x-2))+x^2+8*x-84))

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maxima [B]  time = 0.81, size = 60, normalized size = 2.22 $$\begin{array}{c}{e}^{(\frac{5e^{(x+2)}\log (x)}{4(x{e}^{\left(x^2\right)}+(x{e}^2+14e^2)e^x)}-\frac{5e^{(x+2)}\log (x)}{4(x{e}^{\left(x^2\right)}+(x{e}^2-6e^2)e^x)})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((100*x^2-50*x+50)*log(x)-25)*exp(log(x)+x^2-x-2)^2+((100*x^3+350*x^2-100*x+200)*log(x)-50*x-200)*e
xp(log(x)+x^2-x-2)+(50*x^2+200*x)*log(x)-25*x^2-200*x+2100)*exp(-25*log(x)/(exp(log(x)+x^2-x-2)^2+(2*x+8)*exp(
log(x)+x^2-x-2)+x^2+8*x-84))/(x*exp(log(x)+x^2-x-2)^4+(4*x^2+16*x)*exp(log(x)+x^2-x-2)^3+(6*x^3+48*x^2-104*x)*
exp(log(x)+x^2-x-2)^2+(4*x^4+48*x^3-208*x^2-1344*x)*exp(log(x)+x^2-x-2)+x^5+16*x^4-104*x^3-1344*x^2+7056*x),x,
algorithm="maxima")

[Out]

e^(5/4*e^(x + 2)*log(x)/(x*e^(x^2) + (x*e^2 + 14*e^2)*e^x) - 5/4*e^(x + 2)*log(x)/(x*e^(x^2) + (x*e^2 - 6*e^2)
*e^x))

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mupad [B]  time = 4.81, size = 60, normalized size = 2.22 $$\begin{array}{c}\frac{1}{x^{\frac{25}{8x+x^2+2x^2{\mathrm{e}}^{-x}{\mathrm{e}}^{x^2}{\mathrm{e}}^{-2}+x^2{\mathrm{e}}^{-2x}{\mathrm{e}}^{-4}{\mathrm{e}}^{2x^2}+8x{\mathrm{e}}^{-x}{\mathrm{e}}^{x^2}{\mathrm{e}}^{-2}-84}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(25*log(x))/(8*x + exp(2*log(x) - 2*x + 2*x^2 - 4) + x^2 + exp(log(x) - x + x^2 - 2)*(2*x + 8) - 84
))*(200*x - exp(2*log(x) - 2*x + 2*x^2 - 4)*(log(x)*(100*x^2 - 50*x + 50) - 25) - log(x)*(200*x + 50*x^2) + ex
p(log(x) - x + x^2 - 2)*(50*x - log(x)*(350*x^2 - 100*x + 100*x^3 + 200) + 200) + 25*x^2 - 2100))/(7056*x + ex
p(2*log(x) - 2*x + 2*x^2 - 4)*(48*x^2 - 104*x + 6*x^3) - exp(log(x) - x + x^2 - 2)*(1344*x + 208*x^2 - 48*x^3
- 4*x^4) - 1344*x^2 - 104*x^3 + 16*x^4 + x^5 + exp(3*log(x) - 3*x + 3*x^2 - 6)*(16*x + 4*x^2) + x*exp(4*log(x)
- 4*x + 4*x^2 - 8)),x)

[Out]

1/x^(25/(8*x + x^2 + 2*x^2*exp(-x)*exp(x^2)*exp(-2) + x^2*exp(-2*x)*exp(-4)*exp(2*x^2) + 8*x*exp(-x)*exp(x^2)*
exp(-2) - 84))

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sympy [A]  time = 7.57, size = 46, normalized size = 1.70 $$\begin{array}{c}{e}^{-\frac{25\log (x)}{x^2{e}^{2x^2-2x-4}+x^2+x(2x+8)e^{x^2-x-2}+8x-84}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((100*x**2-50*x+50)*ln(x)-25)*exp(ln(x)+x**2-x-2)**2+((100*x**3+350*x**2-100*x+200)*ln(x)-50*x-200)
*exp(ln(x)+x**2-x-2)+(50*x**2+200*x)*ln(x)-25*x**2-200*x+2100)*exp(-25*ln(x)/(exp(ln(x)+x**2-x-2)**2+(2*x+8)*e
xp(ln(x)+x**2-x-2)+x**2+8*x-84))/(x*exp(ln(x)+x**2-x-2)**4+(4*x**2+16*x)*exp(ln(x)+x**2-x-2)**3+(6*x**3+48*x**
2-104*x)*exp(ln(x)+x**2-x-2)**2+(4*x**4+48*x**3-208*x**2-1344*x)*exp(ln(x)+x**2-x-2)+x**5+16*x**4-104*x**3-134
4*x**2+7056*x),x)

[Out]

exp(-25*log(x)/(x**2*exp(2*x**2 - 2*x - 4) + x**2 + x*(2*x + 8)*exp(x**2 - x - 2) + 8*x - 84))

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