\(\int \frac {e^{-\frac {x^2+(16 x+4 x^2) \log ^2(x)+(64+36 x+4 x^2) \log ^4(x)}{4 \log ^4(x)}} (e^5 (-2 x^2+2 x^3) \log (x-x^2)+e^5 (x^2-x^3) \log (x) \log (x-x^2)+e^5 (-16 x+12 x^2+4 x^3) \log ^2(x) \log (x-x^2)+e^5 (8 x-4 x^2-4 x^3) \log ^3(x) \log (x-x^2)+\log ^5(x) (e^5 (-2+4 x)+e^5 (18 x-14 x^2-4 x^3) \log (x-x^2)))}{(-2 x+2 x^2) \log ^5(x)} \, dx\) [9953]

Optimal result

Integrand size = 207, antiderivative size = 32 \[ \int \frac {e^{-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}} \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{\left (-2 x+2 x^2\right ) \log ^5(x)} \, dx=e^{5-x-\left (4+x+\frac {x}{2 \log ^2(x)}\right )^2} \log \left (x-x^2\right ) \]

[Out]

exp(5)/exp((1/2*x/ln(x)^2+4+x)^2+x)*ln(-x^2+x)

Rubi [F]

\[ \int \frac {e^{-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}} \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{\left (-2 x+2 x^2\right ) \log ^5(x)} \, dx=\int \frac {\exp \left (-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}\right ) \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{\left (-2 x+2 x^2\right ) \log ^5(x)} \, dx \]

[In]

Int[(E^5*(-2*x^2 + 2*x^3)*Log[x - x^2] + E^5*(x^2 - x^3)*Log[x]*Log[x - x^2] + E^5*(-16*x + 12*x^2 + 4*x^3)*Lo
g[x]^2*Log[x - x^2] + E^5*(8*x - 4*x^2 - 4*x^3)*Log[x]^3*Log[x - x^2] + Log[x]^5*(E^5*(-2 + 4*x) + E^5*(18*x -
14*x^2 - 4*x^3)*Log[x - x^2]))/(E^((x^2 + (16*x + 4*x^2)*Log[x]^2 + (64 + 36*x + 4*x^2)*Log[x]^4)/(4*Log[x]^4
))*(-2*x + 2*x^2)*Log[x]^5),x]

[Out]

Defer[Int][E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/Log[x]^2)/(-1 + x), x] + Defer[Int][E^(-11 - 9*
x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/Log[x]^2)/x, x] - 9*Defer[Int][E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4)
- (x*(4 + x))/Log[x]^2)*Log[(1 - x)*x], x] - 2*Defer[Int][E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/
Log[x]^2)*x*Log[(1 - x)*x], x] + Defer[Int][(E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/Log[x]^2)*x*L
og[(1 - x)*x])/Log[x]^5, x] - Defer[Int][(E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/Log[x]^2)*x*Log[
(1 - x)*x])/Log[x]^4, x]/2 + 8*Defer[Int][(E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/Log[x]^2)*Log[(
1 - x)*x])/Log[x]^3, x] + 2*Defer[Int][(E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/Log[x]^2)*x*Log[(1
- x)*x])/Log[x]^3, x] - 4*Defer[Int][(E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/Log[x]^2)*Log[(1 -
x)*x])/Log[x]^2, x] - 2*Defer[Int][(E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/Log[x]^2)*x*Log[(1 - x
)*x])/Log[x]^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}\right ) \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{x (-2+2 x) \log ^5(x)} \, dx \\ & = \int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \left (-2 (-1+x) x^2 \log (-((-1+x) x))+(-1+x) x^2 \log (x) \log (-((-1+x) x))-4 x \left (-4+3 x+x^2\right ) \log ^2(x) \log (-((-1+x) x))+4 x \left (-2+x+x^2\right ) \log ^3(x) \log (-((-1+x) x))+2 \log ^5(x) \left (1-2 x+x \left (-9+7 x+2 x^2\right ) \log (-((-1+x) x))\right )\right )}{2 (1-x) x \log ^5(x)} \, dx \\ & = \frac {1}{2} \int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \left (-2 (-1+x) x^2 \log (-((-1+x) x))+(-1+x) x^2 \log (x) \log (-((-1+x) x))-4 x \left (-4+3 x+x^2\right ) \log ^2(x) \log (-((-1+x) x))+4 x \left (-2+x+x^2\right ) \log ^3(x) \log (-((-1+x) x))+2 \log ^5(x) \left (1-2 x+x \left (-9+7 x+2 x^2\right ) \log (-((-1+x) x))\right )\right )}{(1-x) x \log ^5(x)} \, dx \\ & = \frac {1}{2} \int \left (\frac {2 \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) (-1+2 x)}{(-1+x) x}+\frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \left (2 x-x \log (x)+16 \log ^2(x)+4 x \log ^2(x)-8 \log ^3(x)-4 x \log ^3(x)-18 \log ^5(x)-4 x \log ^5(x)\right ) \log ((1-x) x)}{\log ^5(x)}\right ) \, dx \\ & = \frac {1}{2} \int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \left (2 x-x \log (x)+16 \log ^2(x)+4 x \log ^2(x)-8 \log ^3(x)-4 x \log ^3(x)-18 \log ^5(x)-4 x \log ^5(x)\right ) \log ((1-x) x)}{\log ^5(x)} \, dx+\int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) (-1+2 x)}{(-1+x) x} \, dx \\ & = \frac {1}{2} \int \left (-18 \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \log ((1-x) x)-4 \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x)+\frac {2 \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x)}{\log ^5(x)}-\frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x)}{\log ^4(x)}+\frac {16 \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \log ((1-x) x)}{\log ^3(x)}+\frac {4 \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x)}{\log ^3(x)}-\frac {8 \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \log ((1-x) x)}{\log ^2(x)}-\frac {4 \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x)}{\log ^2(x)}\right ) \, dx+\int \left (\frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right )}{-1+x}+\frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right )}{x}\right ) \, dx \\ & = -\left (\frac {1}{2} \int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x)}{\log ^4(x)} \, dx\right )-2 \int \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x) \, dx+2 \int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x)}{\log ^3(x)} \, dx-2 \int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x)}{\log ^2(x)} \, dx-4 \int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \log ((1-x) x)}{\log ^2(x)} \, dx+8 \int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \log ((1-x) x)}{\log ^3(x)} \, dx-9 \int \exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) \log ((1-x) x) \, dx+\int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right )}{-1+x} \, dx+\int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right )}{x} \, dx+\int \frac {\exp \left (-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}\right ) x \log ((1-x) x)}{\log ^5(x)} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.25 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.28 \[ \int \frac {e^{-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}} \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{\left (-2 x+2 x^2\right ) \log ^5(x)} \, dx=e^{-11-9 x-x^2-\frac {x^2}{4 \log ^4(x)}-\frac {x (4+x)}{\log ^2(x)}} \log (-((-1+x) x)) \]

[In]

Integrate[(E^5*(-2*x^2 + 2*x^3)*Log[x - x^2] + E^5*(x^2 - x^3)*Log[x]*Log[x - x^2] + E^5*(-16*x + 12*x^2 + 4*x
^3)*Log[x]^2*Log[x - x^2] + E^5*(8*x - 4*x^2 - 4*x^3)*Log[x]^3*Log[x - x^2] + Log[x]^5*(E^5*(-2 + 4*x) + E^5*(
18*x - 14*x^2 - 4*x^3)*Log[x - x^2]))/(E^((x^2 + (16*x + 4*x^2)*Log[x]^2 + (64 + 36*x + 4*x^2)*Log[x]^4)/(4*Lo
g[x]^4))*(-2*x + 2*x^2)*Log[x]^5),x]

[Out]

E^(-11 - 9*x - x^2 - x^2/(4*Log[x]^4) - (x*(4 + x))/Log[x]^2)*Log[-((-1 + x)*x)]

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.20 (sec) , antiderivative size = 172, normalized size of antiderivative = 5.38

\[\left (-i {\mathrm e}^{5} \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2}+\frac {i {\mathrm e}^{5} \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{3}}{2}+\frac {i {\mathrm e}^{5} \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i x \right )}{2}+\frac {i {\mathrm e}^{5} \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )\right )}{2}-\frac {i {\mathrm e}^{5} \pi \,\operatorname {csgn}\left (i x \left (-1+x \right )\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i \left (-1+x \right )\right )}{2}+i {\mathrm e}^{5} \pi +{\mathrm e}^{5} \ln \left (x \right )+{\mathrm e}^{5} \ln \left (-1+x \right )\right ) {\mathrm e}^{-\frac {4 x^{2} \ln \left (x \right )^{4}+36 x \ln \left (x \right )^{4}+64 \ln \left (x \right )^{4}+4 x^{2} \ln \left (x \right )^{2}+16 x \ln \left (x \right )^{2}+x^{2}}{4 \ln \left (x \right )^{4}}}\]

[In]

int((((-4*x^3-14*x^2+18*x)*exp(5)*ln(-x^2+x)+(4*x-2)*exp(5))*ln(x)^5+(-4*x^3-4*x^2+8*x)*exp(5)*ln(-x^2+x)*ln(x
)^3+(4*x^3+12*x^2-16*x)*exp(5)*ln(-x^2+x)*ln(x)^2+(-x^3+x^2)*exp(5)*ln(-x^2+x)*ln(x)+(2*x^3-2*x^2)*exp(5)*ln(-
x^2+x))/(2*x^2-2*x)/ln(x)^5/exp(1/4*((4*x^2+36*x+64)*ln(x)^4+(4*x^2+16*x)*ln(x)^2+x^2)/ln(x)^4),x)

[Out]

(-I*exp(5)*Pi*csgn(I*x*(-1+x))^2+1/2*I*exp(5)*Pi*csgn(I*x*(-1+x))^3+1/2*I*exp(5)*Pi*csgn(I*x*(-1+x))^2*csgn(I*
x)+1/2*I*exp(5)*Pi*csgn(I*x*(-1+x))^2*csgn(I*(-1+x))-1/2*I*exp(5)*Pi*csgn(I*x*(-1+x))*csgn(I*x)*csgn(I*(-1+x))
+I*exp(5)*Pi+exp(5)*ln(x)+exp(5)*ln(-1+x))*exp(-1/4*(4*x^2*ln(x)^4+36*x*ln(x)^4+64*ln(x)^4+4*x^2*ln(x)^2+16*x*
ln(x)^2+x^2)/ln(x)^4)

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.53 \[ \int \frac {e^{-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}} \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{\left (-2 x+2 x^2\right ) \log ^5(x)} \, dx=e^{\left (-\frac {4 \, {\left (x^{2} + 9 \, x + 16\right )} \log \left (x\right )^{4} + 4 \, {\left (x^{2} + 4 \, x\right )} \log \left (x\right )^{2} + x^{2}}{4 \, \log \left (x\right )^{4}} + 5\right )} \log \left (-x^{2} + x\right ) \]

[In]

integrate((((-4*x^3-14*x^2+18*x)*exp(5)*log(-x^2+x)+(4*x-2)*exp(5))*log(x)^5+(-4*x^3-4*x^2+8*x)*exp(5)*log(-x^
2+x)*log(x)^3+(4*x^3+12*x^2-16*x)*exp(5)*log(-x^2+x)*log(x)^2+(-x^3+x^2)*exp(5)*log(-x^2+x)*log(x)+(2*x^3-2*x^
2)*exp(5)*log(-x^2+x))/(2*x^2-2*x)/log(x)^5/exp(1/4*((4*x^2+36*x+64)*log(x)^4+(4*x^2+16*x)*log(x)^2+x^2)/log(x
)^4),x, algorithm="fricas")

[Out]

e^(-1/4*(4*(x^2 + 9*x + 16)*log(x)^4 + 4*(x^2 + 4*x)*log(x)^2 + x^2)/log(x)^4 + 5)*log(-x^2 + x)

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}} \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{\left (-2 x+2 x^2\right ) \log ^5(x)} \, dx=\text {Timed out} \]

[In]

integrate((((-4*x**3-14*x**2+18*x)*exp(5)*ln(-x**2+x)+(4*x-2)*exp(5))*ln(x)**5+(-4*x**3-4*x**2+8*x)*exp(5)*ln(
-x**2+x)*ln(x)**3+(4*x**3+12*x**2-16*x)*exp(5)*ln(-x**2+x)*ln(x)**2+(-x**3+x**2)*exp(5)*ln(-x**2+x)*ln(x)+(2*x
**3-2*x**2)*exp(5)*ln(-x**2+x))/(2*x**2-2*x)/ln(x)**5/exp(1/4*((4*x**2+36*x+64)*ln(x)**4+(4*x**2+16*x)*ln(x)**
2+x**2)/ln(x)**4),x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.47 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.44 \[ \int \frac {e^{-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}} \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{\left (-2 x+2 x^2\right ) \log ^5(x)} \, dx={\left (\log \left (x\right ) + \log \left (-x + 1\right )\right )} e^{\left (-x^{2} - 9 \, x - \frac {x^{2}}{\log \left (x\right )^{2}} - \frac {4 \, x}{\log \left (x\right )^{2}} - \frac {x^{2}}{4 \, \log \left (x\right )^{4}} - 11\right )} \]

[In]

integrate((((-4*x^3-14*x^2+18*x)*exp(5)*log(-x^2+x)+(4*x-2)*exp(5))*log(x)^5+(-4*x^3-4*x^2+8*x)*exp(5)*log(-x^
2+x)*log(x)^3+(4*x^3+12*x^2-16*x)*exp(5)*log(-x^2+x)*log(x)^2+(-x^3+x^2)*exp(5)*log(-x^2+x)*log(x)+(2*x^3-2*x^
2)*exp(5)*log(-x^2+x))/(2*x^2-2*x)/log(x)^5/exp(1/4*((4*x^2+36*x+64)*log(x)^4+(4*x^2+16*x)*log(x)^2+x^2)/log(x
)^4),x, algorithm="maxima")

[Out]

(log(x) + log(-x + 1))*e^(-x^2 - 9*x - x^2/log(x)^2 - 4*x/log(x)^2 - 1/4*x^2/log(x)^4 - 11)

Giac [F]

\[ \int \frac {e^{-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}} \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{\left (-2 x+2 x^2\right ) \log ^5(x)} \, dx=\int { -\frac {{\left (4 \, {\left (x^{3} + x^{2} - 2 \, x\right )} e^{5} \log \left (-x^{2} + x\right ) \log \left (x\right )^{3} + 2 \, {\left ({\left (2 \, x^{3} + 7 \, x^{2} - 9 \, x\right )} e^{5} \log \left (-x^{2} + x\right ) - {\left (2 \, x - 1\right )} e^{5}\right )} \log \left (x\right )^{5} - 4 \, {\left (x^{3} + 3 \, x^{2} - 4 \, x\right )} e^{5} \log \left (-x^{2} + x\right ) \log \left (x\right )^{2} + {\left (x^{3} - x^{2}\right )} e^{5} \log \left (-x^{2} + x\right ) \log \left (x\right ) - 2 \, {\left (x^{3} - x^{2}\right )} e^{5} \log \left (-x^{2} + x\right )\right )} e^{\left (-\frac {4 \, {\left (x^{2} + 9 \, x + 16\right )} \log \left (x\right )^{4} + 4 \, {\left (x^{2} + 4 \, x\right )} \log \left (x\right )^{2} + x^{2}}{4 \, \log \left (x\right )^{4}}\right )}}{2 \, {\left (x^{2} - x\right )} \log \left (x\right )^{5}} \,d x } \]

[In]

integrate((((-4*x^3-14*x^2+18*x)*exp(5)*log(-x^2+x)+(4*x-2)*exp(5))*log(x)^5+(-4*x^3-4*x^2+8*x)*exp(5)*log(-x^
2+x)*log(x)^3+(4*x^3+12*x^2-16*x)*exp(5)*log(-x^2+x)*log(x)^2+(-x^3+x^2)*exp(5)*log(-x^2+x)*log(x)+(2*x^3-2*x^
2)*exp(5)*log(-x^2+x))/(2*x^2-2*x)/log(x)^5/exp(1/4*((4*x^2+36*x+64)*log(x)^4+(4*x^2+16*x)*log(x)^2+x^2)/log(x
)^4),x, algorithm="giac")

[Out]

undef

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{-\frac {x^2+\left (16 x+4 x^2\right ) \log ^2(x)+\left (64+36 x+4 x^2\right ) \log ^4(x)}{4 \log ^4(x)}} \left (e^5 \left (-2 x^2+2 x^3\right ) \log \left (x-x^2\right )+e^5 \left (x^2-x^3\right ) \log (x) \log \left (x-x^2\right )+e^5 \left (-16 x+12 x^2+4 x^3\right ) \log ^2(x) \log \left (x-x^2\right )+e^5 \left (8 x-4 x^2-4 x^3\right ) \log ^3(x) \log \left (x-x^2\right )+\log ^5(x) \left (e^5 (-2+4 x)+e^5 \left (18 x-14 x^2-4 x^3\right ) \log \left (x-x^2\right )\right )\right )}{\left (-2 x+2 x^2\right ) \log ^5(x)} \, dx=\int -\frac {{\mathrm {e}}^{-\frac {\frac {{\ln \left (x\right )}^2\,\left (4\,x^2+16\,x\right )}{4}+\frac {{\ln \left (x\right )}^4\,\left (4\,x^2+36\,x+64\right )}{4}+\frac {x^2}{4}}{{\ln \left (x\right )}^4}}\,\left (\left ({\mathrm {e}}^5\,\left (4\,x-2\right )-{\mathrm {e}}^5\,\ln \left (x-x^2\right )\,\left (4\,x^3+14\,x^2-18\,x\right )\right )\,{\ln \left (x\right )}^5-{\mathrm {e}}^5\,\ln \left (x-x^2\right )\,\left (4\,x^3+4\,x^2-8\,x\right )\,{\ln \left (x\right )}^3+{\mathrm {e}}^5\,\ln \left (x-x^2\right )\,\left (4\,x^3+12\,x^2-16\,x\right )\,{\ln \left (x\right )}^2+{\mathrm {e}}^5\,\ln \left (x-x^2\right )\,\left (x^2-x^3\right )\,\ln \left (x\right )-{\mathrm {e}}^5\,\ln \left (x-x^2\right )\,\left (2\,x^2-2\,x^3\right )\right )}{{\ln \left (x\right )}^5\,\left (2\,x-2\,x^2\right )} \,d x \]

[In]

int(-(exp(-((log(x)^2*(16*x + 4*x^2))/4 + (log(x)^4*(36*x + 4*x^2 + 64))/4 + x^2/4)/log(x)^4)*(log(x)^5*(exp(5
)*(4*x - 2) - exp(5)*log(x - x^2)*(14*x^2 - 18*x + 4*x^3)) - exp(5)*log(x - x^2)*(2*x^2 - 2*x^3) - exp(5)*log(
x - x^2)*log(x)^3*(4*x^2 - 8*x + 4*x^3) + exp(5)*log(x - x^2)*log(x)^2*(12*x^2 - 16*x + 4*x^3) + exp(5)*log(x
- x^2)*log(x)*(x^2 - x^3)))/(log(x)^5*(2*x - 2*x^2)),x)

[Out]

int(-(exp(-((log(x)^2*(16*x + 4*x^2))/4 + (log(x)^4*(36*x + 4*x^2 + 64))/4 + x^2/4)/log(x)^4)*(log(x)^5*(exp(5
)*(4*x - 2) - exp(5)*log(x - x^2)*(14*x^2 - 18*x + 4*x^3)) - exp(5)*log(x - x^2)*(2*x^2 - 2*x^3) - exp(5)*log(
x - x^2)*log(x)^3*(4*x^2 - 8*x + 4*x^3) + exp(5)*log(x - x^2)*log(x)^2*(12*x^2 - 16*x + 4*x^3) + exp(5)*log(x
- x^2)*log(x)*(x^2 - x^3)))/(log(x)^5*(2*x - 2*x^2)), x)