\(\int \frac {e^{x^2} (-20 x+30 x^2-10 x^3+10 x^4)+e^{x^2} (-30 x+40 x^2-20 x^3+20 x^4) \log (-x+x^2)+e^{x^2} (-10 x+10 x^2-10 x^3+10 x^4) \log ^2(-x+x^2)}{-4+4 x+e^{x^2} (4 x^2-4 x^3)+e^{2 x^2} (-x^4+x^5)+(e^{x^2} (8 x^2-8 x^3)+e^{2 x^2} (-4 x^4+4 x^5)) \log (-x+x^2)+(e^{x^2} (4 x^2-4 x^3)+e^{2 x^2} (-6 x^4+6 x^5)) \log ^2(-x+x^2)+e^{2 x^2} (-4 x^4+4 x^5) \log ^3(-x+x^2)+e^{2 x^2} (-x^4+x^5) \log ^4(-x+x^2)} \, dx\) [6145]

Optimal result

Integrand size = 286, antiderivative size = 27 \[ \int \frac {e^{x^2} \left (-20 x+30 x^2-10 x^3+10 x^4\right )+e^{x^2} \left (-30 x+40 x^2-20 x^3+20 x^4\right ) \log \left (-x+x^2\right )+e^{x^2} \left (-10 x+10 x^2-10 x^3+10 x^4\right ) \log ^2\left (-x+x^2\right )}{-4+4 x+e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-x^4+x^5\right )+\left (e^{x^2} \left (8 x^2-8 x^3\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right )\right ) \log \left (-x+x^2\right )+\left (e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-6 x^4+6 x^5\right )\right ) \log ^2\left (-x+x^2\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right ) \log ^3\left (-x+x^2\right )+e^{2 x^2} \left (-x^4+x^5\right ) \log ^4\left (-x+x^2\right )} \, dx=\frac {5}{2-e^{x^2} \left (x+x \log \left (-x+x^2\right )\right )^2} \]

[Out]

5/(2-(x+x*ln(x^2-x))^2*exp(x^2))

Rubi [F]

\[ \int \frac {e^{x^2} \left (-20 x+30 x^2-10 x^3+10 x^4\right )+e^{x^2} \left (-30 x+40 x^2-20 x^3+20 x^4\right ) \log \left (-x+x^2\right )+e^{x^2} \left (-10 x+10 x^2-10 x^3+10 x^4\right ) \log ^2\left (-x+x^2\right )}{-4+4 x+e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-x^4+x^5\right )+\left (e^{x^2} \left (8 x^2-8 x^3\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right )\right ) \log \left (-x+x^2\right )+\left (e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-6 x^4+6 x^5\right )\right ) \log ^2\left (-x+x^2\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right ) \log ^3\left (-x+x^2\right )+e^{2 x^2} \left (-x^4+x^5\right ) \log ^4\left (-x+x^2\right )} \, dx=\int \frac {e^{x^2} \left (-20 x+30 x^2-10 x^3+10 x^4\right )+e^{x^2} \left (-30 x+40 x^2-20 x^3+20 x^4\right ) \log \left (-x+x^2\right )+e^{x^2} \left (-10 x+10 x^2-10 x^3+10 x^4\right ) \log ^2\left (-x+x^2\right )}{-4+4 x+e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-x^4+x^5\right )+\left (e^{x^2} \left (8 x^2-8 x^3\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right )\right ) \log \left (-x+x^2\right )+\left (e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-6 x^4+6 x^5\right )\right ) \log ^2\left (-x+x^2\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right ) \log ^3\left (-x+x^2\right )+e^{2 x^2} \left (-x^4+x^5\right ) \log ^4\left (-x+x^2\right )} \, dx \]

[In]

Int[(E^x^2*(-20*x + 30*x^2 - 10*x^3 + 10*x^4) + E^x^2*(-30*x + 40*x^2 - 20*x^3 + 20*x^4)*Log[-x + x^2] + E^x^2
*(-10*x + 10*x^2 - 10*x^3 + 10*x^4)*Log[-x + x^2]^2)/(-4 + 4*x + E^x^2*(4*x^2 - 4*x^3) + E^(2*x^2)*(-x^4 + x^5
) + (E^x^2*(8*x^2 - 8*x^3) + E^(2*x^2)*(-4*x^4 + 4*x^5))*Log[-x + x^2] + (E^x^2*(4*x^2 - 4*x^3) + E^(2*x^2)*(-
6*x^4 + 6*x^5))*Log[-x + x^2]^2 + E^(2*x^2)*(-4*x^4 + 4*x^5)*Log[-x + x^2]^3 + E^(2*x^2)*(-x^4 + x^5)*Log[-x +
x^2]^4),x]

[Out]

10*Defer[Int][E^x^2/(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Log[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*x]^2)^2, x] + 10*De
fer[Int][E^x^2/((-1 + x)*(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Log[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*x]^2)^2), x] +
30*Defer[Int][(E^x^2*x)/(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Log[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*x]^2)^2, x] +
10*Defer[Int][(E^x^2*x^3)/(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Log[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*x]^2)^2, x] +
10*Defer[Int][(E^x^2*Log[(-1 + x)*x])/(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Log[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*
x]^2)^2, x] + 10*Defer[Int][(E^x^2*Log[(-1 + x)*x])/((-1 + x)*(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Log[(-1 + x)*x] +
E^x^2*x^2*Log[(-1 + x)*x]^2)^2), x] + 40*Defer[Int][(E^x^2*x*Log[(-1 + x)*x])/(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Lo
g[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*x]^2)^2, x] + 20*Defer[Int][(E^x^2*x^3*Log[(-1 + x)*x])/(-2 + E^x^2*x^2
+ 2*E^x^2*x^2*Log[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*x]^2)^2, x] + 10*Defer[Int][(E^x^2*x*Log[(-1 + x)*x]^2
)/(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Log[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*x]^2)^2, x] + 10*Defer[Int][(E^x^2*x^
3*Log[(-1 + x)*x]^2)/(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Log[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*x]^2)^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {10 e^{x^2} x (1+\log ((-1+x) x)) \left (2-3 x+x^2-x^3-\left (-1+x-x^2+x^3\right ) \log ((-1+x) x)\right )}{(1-x) \left (2-e^{x^2} x^2-2 e^{x^2} x^2 \log ((-1+x) x)-e^{x^2} x^2 \log ^2((-1+x) x)\right )^2} \, dx \\ & = 10 \int \frac {e^{x^2} x (1+\log ((-1+x) x)) \left (2-3 x+x^2-x^3-\left (-1+x-x^2+x^3\right ) \log ((-1+x) x)\right )}{(1-x) \left (2-e^{x^2} x^2-2 e^{x^2} x^2 \log ((-1+x) x)-e^{x^2} x^2 \log ^2((-1+x) x)\right )^2} \, dx \\ & = 10 \int \left (\frac {e^{x^2} (1+\log ((-1+x) x)) \left (-2+3 x-x^2+x^3-\log ((-1+x) x)+x \log ((-1+x) x)-x^2 \log ((-1+x) x)+x^3 \log ((-1+x) x)\right )}{\left (-2+e^{x^2} x^2+2 e^{x^2} x^2 \log ((-1+x) x)+e^{x^2} x^2 \log ^2((-1+x) x)\right )^2}+\frac {e^{x^2} (1+\log ((-1+x) x)) \left (-2+3 x-x^2+x^3-\log ((-1+x) x)+x \log ((-1+x) x)-x^2 \log ((-1+x) x)+x^3 \log ((-1+x) x)\right )}{(-1+x) \left (-2+e^{x^2} x^2+2 e^{x^2} x^2 \log ((-1+x) x)+e^{x^2} x^2 \log ^2((-1+x) x)\right )^2}\right ) \, dx \\ & = 10 \int \frac {e^{x^2} (1+\log ((-1+x) x)) \left (-2+3 x-x^2+x^3-\log ((-1+x) x)+x \log ((-1+x) x)-x^2 \log ((-1+x) x)+x^3 \log ((-1+x) x)\right )}{\left (-2+e^{x^2} x^2+2 e^{x^2} x^2 \log ((-1+x) x)+e^{x^2} x^2 \log ^2((-1+x) x)\right )^2} \, dx+10 \int \frac {e^{x^2} (1+\log ((-1+x) x)) \left (-2+3 x-x^2+x^3-\log ((-1+x) x)+x \log ((-1+x) x)-x^2 \log ((-1+x) x)+x^3 \log ((-1+x) x)\right )}{(-1+x) \left (-2+e^{x^2} x^2+2 e^{x^2} x^2 \log ((-1+x) x)+e^{x^2} x^2 \log ^2((-1+x) x)\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.12 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.78 \[ \int \frac {e^{x^2} \left (-20 x+30 x^2-10 x^3+10 x^4\right )+e^{x^2} \left (-30 x+40 x^2-20 x^3+20 x^4\right ) \log \left (-x+x^2\right )+e^{x^2} \left (-10 x+10 x^2-10 x^3+10 x^4\right ) \log ^2\left (-x+x^2\right )}{-4+4 x+e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-x^4+x^5\right )+\left (e^{x^2} \left (8 x^2-8 x^3\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right )\right ) \log \left (-x+x^2\right )+\left (e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-6 x^4+6 x^5\right )\right ) \log ^2\left (-x+x^2\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right ) \log ^3\left (-x+x^2\right )+e^{2 x^2} \left (-x^4+x^5\right ) \log ^4\left (-x+x^2\right )} \, dx=-\frac {5}{-2+e^{x^2} x^2+2 e^{x^2} x^2 \log ((-1+x) x)+e^{x^2} x^2 \log ^2((-1+x) x)} \]

[In]

Integrate[(E^x^2*(-20*x + 30*x^2 - 10*x^3 + 10*x^4) + E^x^2*(-30*x + 40*x^2 - 20*x^3 + 20*x^4)*Log[-x + x^2] +
E^x^2*(-10*x + 10*x^2 - 10*x^3 + 10*x^4)*Log[-x + x^2]^2)/(-4 + 4*x + E^x^2*(4*x^2 - 4*x^3) + E^(2*x^2)*(-x^4
+ x^5) + (E^x^2*(8*x^2 - 8*x^3) + E^(2*x^2)*(-4*x^4 + 4*x^5))*Log[-x + x^2] + (E^x^2*(4*x^2 - 4*x^3) + E^(2*x
^2)*(-6*x^4 + 6*x^5))*Log[-x + x^2]^2 + E^(2*x^2)*(-4*x^4 + 4*x^5)*Log[-x + x^2]^3 + E^(2*x^2)*(-x^4 + x^5)*Lo
g[-x + x^2]^4),x]

[Out]

-5/(-2 + E^x^2*x^2 + 2*E^x^2*x^2*Log[(-1 + x)*x] + E^x^2*x^2*Log[(-1 + x)*x]^2)

Maple [A] (verified)

Time = 8.44 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.85

method	result	size
parallelrisch	\(-\frac {5}{\ln \left (x^{2}-x \right )^{2} {\mathrm e}^{x^{2}} x^{2}+2 \ln \left (x^{2}-x \right ) {\mathrm e}^{x^{2}} x^{2}+x^{2} {\mathrm e}^{x^{2}}-2}\)	\(50\)
risch	\(\text {Expression too large to display}\)	\(703\)

[In]

int(((10*x^4-10*x^3+10*x^2-10*x)*exp(x^2)*ln(x^2-x)^2+(20*x^4-20*x^3+40*x^2-30*x)*exp(x^2)*ln(x^2-x)+(10*x^4-1
0*x^3+30*x^2-20*x)*exp(x^2))/((x^5-x^4)*exp(x^2)^2*ln(x^2-x)^4+(4*x^5-4*x^4)*exp(x^2)^2*ln(x^2-x)^3+((6*x^5-6*
x^4)*exp(x^2)^2+(-4*x^3+4*x^2)*exp(x^2))*ln(x^2-x)^2+((4*x^5-4*x^4)*exp(x^2)^2+(-8*x^3+8*x^2)*exp(x^2))*ln(x^2
-x)+(x^5-x^4)*exp(x^2)^2+(-4*x^3+4*x^2)*exp(x^2)+4*x-4),x,method=_RETURNVERBOSE)

[Out]

-5/(ln(x^2-x)^2*exp(x^2)*x^2+2*ln(x^2-x)*exp(x^2)*x^2+x^2*exp(x^2)-2)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.81 \[ \int \frac {e^{x^2} \left (-20 x+30 x^2-10 x^3+10 x^4\right )+e^{x^2} \left (-30 x+40 x^2-20 x^3+20 x^4\right ) \log \left (-x+x^2\right )+e^{x^2} \left (-10 x+10 x^2-10 x^3+10 x^4\right ) \log ^2\left (-x+x^2\right )}{-4+4 x+e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-x^4+x^5\right )+\left (e^{x^2} \left (8 x^2-8 x^3\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right )\right ) \log \left (-x+x^2\right )+\left (e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-6 x^4+6 x^5\right )\right ) \log ^2\left (-x+x^2\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right ) \log ^3\left (-x+x^2\right )+e^{2 x^2} \left (-x^4+x^5\right ) \log ^4\left (-x+x^2\right )} \, dx=-\frac {5}{x^{2} e^{\left (x^{2}\right )} \log \left (x^{2} - x\right )^{2} + 2 \, x^{2} e^{\left (x^{2}\right )} \log \left (x^{2} - x\right ) + x^{2} e^{\left (x^{2}\right )} - 2} \]

[In]

integrate(((10*x^4-10*x^3+10*x^2-10*x)*exp(x^2)*log(x^2-x)^2+(20*x^4-20*x^3+40*x^2-30*x)*exp(x^2)*log(x^2-x)+(
10*x^4-10*x^3+30*x^2-20*x)*exp(x^2))/((x^5-x^4)*exp(x^2)^2*log(x^2-x)^4+(4*x^5-4*x^4)*exp(x^2)^2*log(x^2-x)^3+
((6*x^5-6*x^4)*exp(x^2)^2+(-4*x^3+4*x^2)*exp(x^2))*log(x^2-x)^2+((4*x^5-4*x^4)*exp(x^2)^2+(-8*x^3+8*x^2)*exp(x
^2))*log(x^2-x)+(x^5-x^4)*exp(x^2)^2+(-4*x^3+4*x^2)*exp(x^2)+4*x-4),x, algorithm="fricas")

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.33 \[ \int \frac {e^{x^2} \left (-20 x+30 x^2-10 x^3+10 x^4\right )+e^{x^2} \left (-30 x+40 x^2-20 x^3+20 x^4\right ) \log \left (-x+x^2\right )+e^{x^2} \left (-10 x+10 x^2-10 x^3+10 x^4\right ) \log ^2\left (-x+x^2\right )}{-4+4 x+e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-x^4+x^5\right )+\left (e^{x^2} \left (8 x^2-8 x^3\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right )\right ) \log \left (-x+x^2\right )+\left (e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-6 x^4+6 x^5\right )\right ) \log ^2\left (-x+x^2\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right ) \log ^3\left (-x+x^2\right )+e^{2 x^2} \left (-x^4+x^5\right ) \log ^4\left (-x+x^2\right )} \, dx=- \frac {5}{\left (x^{2} \log {\left (x^{2} - x \right )}^{2} + 2 x^{2} \log {\left (x^{2} - x \right )} + x^{2}\right ) e^{x^{2}} - 2} \]

[In]

integrate(((10*x**4-10*x**3+10*x**2-10*x)*exp(x**2)*ln(x**2-x)**2+(20*x**4-20*x**3+40*x**2-30*x)*exp(x**2)*ln(
x**2-x)+(10*x**4-10*x**3+30*x**2-20*x)*exp(x**2))/((x**5-x**4)*exp(x**2)**2*ln(x**2-x)**4+(4*x**5-4*x**4)*exp(
x**2)**2*ln(x**2-x)**3+((6*x**5-6*x**4)*exp(x**2)**2+(-4*x**3+4*x**2)*exp(x**2))*ln(x**2-x)**2+((4*x**5-4*x**4
)*exp(x**2)**2+(-8*x**3+8*x**2)*exp(x**2))*ln(x**2-x)+(x**5-x**4)*exp(x**2)**2+(-4*x**3+4*x**2)*exp(x**2)+4*x-
4),x)

[Out]

-5/((x**2*log(x**2 - x)**2 + 2*x**2*log(x**2 - x) + x**2)*exp(x**2) - 2)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (25) = 50\).

Time = 0.27 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.07 \[ \int \frac {e^{x^2} \left (-20 x+30 x^2-10 x^3+10 x^4\right )+e^{x^2} \left (-30 x+40 x^2-20 x^3+20 x^4\right ) \log \left (-x+x^2\right )+e^{x^2} \left (-10 x+10 x^2-10 x^3+10 x^4\right ) \log ^2\left (-x+x^2\right )}{-4+4 x+e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-x^4+x^5\right )+\left (e^{x^2} \left (8 x^2-8 x^3\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right )\right ) \log \left (-x+x^2\right )+\left (e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-6 x^4+6 x^5\right )\right ) \log ^2\left (-x+x^2\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right ) \log ^3\left (-x+x^2\right )+e^{2 x^2} \left (-x^4+x^5\right ) \log ^4\left (-x+x^2\right )} \, dx=-\frac {5}{{\left (x^{2} \log \left (x - 1\right )^{2} + x^{2} \log \left (x\right )^{2} + 2 \, x^{2} \log \left (x\right ) + x^{2} + 2 \, {\left (x^{2} \log \left (x\right ) + x^{2}\right )} \log \left (x - 1\right )\right )} e^{\left (x^{2}\right )} - 2} \]

[In]

integrate(((10*x^4-10*x^3+10*x^2-10*x)*exp(x^2)*log(x^2-x)^2+(20*x^4-20*x^3+40*x^2-30*x)*exp(x^2)*log(x^2-x)+(
10*x^4-10*x^3+30*x^2-20*x)*exp(x^2))/((x^5-x^4)*exp(x^2)^2*log(x^2-x)^4+(4*x^5-4*x^4)*exp(x^2)^2*log(x^2-x)^3+
((6*x^5-6*x^4)*exp(x^2)^2+(-4*x^3+4*x^2)*exp(x^2))*log(x^2-x)^2+((4*x^5-4*x^4)*exp(x^2)^2+(-8*x^3+8*x^2)*exp(x
^2))*log(x^2-x)+(x^5-x^4)*exp(x^2)^2+(-4*x^3+4*x^2)*exp(x^2)+4*x-4),x, algorithm="maxima")

[Out]

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

Giac [A] (verification not implemented)

none

Time = 0.67 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.81 \[ \int \frac {e^{x^2} \left (-20 x+30 x^2-10 x^3+10 x^4\right )+e^{x^2} \left (-30 x+40 x^2-20 x^3+20 x^4\right ) \log \left (-x+x^2\right )+e^{x^2} \left (-10 x+10 x^2-10 x^3+10 x^4\right ) \log ^2\left (-x+x^2\right )}{-4+4 x+e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-x^4+x^5\right )+\left (e^{x^2} \left (8 x^2-8 x^3\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right )\right ) \log \left (-x+x^2\right )+\left (e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-6 x^4+6 x^5\right )\right ) \log ^2\left (-x+x^2\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right ) \log ^3\left (-x+x^2\right )+e^{2 x^2} \left (-x^4+x^5\right ) \log ^4\left (-x+x^2\right )} \, dx=-\frac {5}{x^{2} e^{\left (x^{2}\right )} \log \left (x^{2} - x\right )^{2} + 2 \, x^{2} e^{\left (x^{2}\right )} \log \left (x^{2} - x\right ) + x^{2} e^{\left (x^{2}\right )} - 2} \]

[In]

integrate(((10*x^4-10*x^3+10*x^2-10*x)*exp(x^2)*log(x^2-x)^2+(20*x^4-20*x^3+40*x^2-30*x)*exp(x^2)*log(x^2-x)+(
10*x^4-10*x^3+30*x^2-20*x)*exp(x^2))/((x^5-x^4)*exp(x^2)^2*log(x^2-x)^4+(4*x^5-4*x^4)*exp(x^2)^2*log(x^2-x)^3+
((6*x^5-6*x^4)*exp(x^2)^2+(-4*x^3+4*x^2)*exp(x^2))*log(x^2-x)^2+((4*x^5-4*x^4)*exp(x^2)^2+(-8*x^3+8*x^2)*exp(x
^2))*log(x^2-x)+(x^5-x^4)*exp(x^2)^2+(-4*x^3+4*x^2)*exp(x^2)+4*x-4),x, algorithm="giac")

[Out]

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

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{x^2} \left (-20 x+30 x^2-10 x^3+10 x^4\right )+e^{x^2} \left (-30 x+40 x^2-20 x^3+20 x^4\right ) \log \left (-x+x^2\right )+e^{x^2} \left (-10 x+10 x^2-10 x^3+10 x^4\right ) \log ^2\left (-x+x^2\right )}{-4+4 x+e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-x^4+x^5\right )+\left (e^{x^2} \left (8 x^2-8 x^3\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right )\right ) \log \left (-x+x^2\right )+\left (e^{x^2} \left (4 x^2-4 x^3\right )+e^{2 x^2} \left (-6 x^4+6 x^5\right )\right ) \log ^2\left (-x+x^2\right )+e^{2 x^2} \left (-4 x^4+4 x^5\right ) \log ^3\left (-x+x^2\right )+e^{2 x^2} \left (-x^4+x^5\right ) \log ^4\left (-x+x^2\right )} \, dx=-\int \frac {{\mathrm {e}}^{x^2}\,\left (-10\,x^4+10\,x^3-10\,x^2+10\,x\right )\,{\ln \left (x^2-x\right )}^2+{\mathrm {e}}^{x^2}\,\left (-20\,x^4+20\,x^3-40\,x^2+30\,x\right )\,\ln \left (x^2-x\right )+{\mathrm {e}}^{x^2}\,\left (-10\,x^4+10\,x^3-30\,x^2+20\,x\right )}{-{\mathrm {e}}^{2\,x^2}\,\left (x^4-x^5\right )\,{\ln \left (x^2-x\right )}^4-{\mathrm {e}}^{2\,x^2}\,\left (4\,x^4-4\,x^5\right )\,{\ln \left (x^2-x\right )}^3+\left ({\mathrm {e}}^{x^2}\,\left (4\,x^2-4\,x^3\right )-{\mathrm {e}}^{2\,x^2}\,\left (6\,x^4-6\,x^5\right )\right )\,{\ln \left (x^2-x\right )}^2+\left ({\mathrm {e}}^{x^2}\,\left (8\,x^2-8\,x^3\right )-{\mathrm {e}}^{2\,x^2}\,\left (4\,x^4-4\,x^5\right )\right )\,\ln \left (x^2-x\right )+4\,x-{\mathrm {e}}^{2\,x^2}\,\left (x^4-x^5\right )+{\mathrm {e}}^{x^2}\,\left (4\,x^2-4\,x^3\right )-4} \,d x \]

[In]

int(-(exp(x^2)*(20*x - 30*x^2 + 10*x^3 - 10*x^4) + exp(x^2)*log(x^2 - x)^2*(10*x - 10*x^2 + 10*x^3 - 10*x^4) +
exp(x^2)*log(x^2 - x)*(30*x - 40*x^2 + 20*x^3 - 20*x^4))/(4*x - exp(2*x^2)*(x^4 - x^5) + exp(x^2)*(4*x^2 - 4*
x^3) + log(x^2 - x)*(exp(x^2)*(8*x^2 - 8*x^3) - exp(2*x^2)*(4*x^4 - 4*x^5)) + log(x^2 - x)^2*(exp(x^2)*(4*x^2
- 4*x^3) - exp(2*x^2)*(6*x^4 - 6*x^5)) - exp(2*x^2)*log(x^2 - x)^4*(x^4 - x^5) - exp(2*x^2)*log(x^2 - x)^3*(4*
x^4 - 4*x^5) - 4),x)

[Out]

-int((exp(x^2)*(20*x - 30*x^2 + 10*x^3 - 10*x^4) + exp(x^2)*log(x^2 - x)^2*(10*x - 10*x^2 + 10*x^3 - 10*x^4) +
exp(x^2)*log(x^2 - x)*(30*x - 40*x^2 + 20*x^3 - 20*x^4))/(4*x - exp(2*x^2)*(x^4 - x^5) + exp(x^2)*(4*x^2 - 4*
x^3) + log(x^2 - x)*(exp(x^2)*(8*x^2 - 8*x^3) - exp(2*x^2)*(4*x^4 - 4*x^5)) + log(x^2 - x)^2*(exp(x^2)*(4*x^2
- 4*x^3) - exp(2*x^2)*(6*x^4 - 6*x^5)) - exp(2*x^2)*log(x^2 - x)^4*(x^4 - x^5) - exp(2*x^2)*log(x^2 - x)^3*(4*
x^4 - 4*x^5) - 4), x)