\(\int \frac {e^{\frac {1}{-x-4 \log (3)+\log (x+e^x \log (x^2))}} (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)) \log (x^2)+(-4 x^3-16 x^2 \log (3)+e^x (-4 x^2-16 x \log (3)) \log (x^2)) \log (x+e^x \log (x^2))+(2 x^2+2 e^x x \log (x^2)) \log ^2(x+e^x \log (x^2)))}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x (x^3+8 x^2 \log (3)+16 x \log ^2(3)) \log (x^2)+(-2 x^3-8 x^2 \log (3)+e^x (-2 x^2-8 x \log (3)) \log (x^2)) \log (x+e^x \log (x^2))+(x^2+e^x x \log (x^2)) \log ^2(x+e^x \log (x^2))} \, dx\) [1659]

Optimal result

Integrand size = 289, antiderivative size = 28 \[ \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx=2 e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} (4+x) \]

[Out]

2*(4+x)*exp(1/(ln(exp(x)*ln(x^2)+x)-4*ln(3)-x))

Rubi [F]

\[ \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx=\int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx \]

[In]

Int[(E^(-x - 4*Log[3] + Log[x + E^x*Log[x^2]])^(-1)*(E^x*(-16 - 4*x) - 8*x + 6*x^2 + 2*x^3 + 2*x^4 + 16*x^3*Lo
g[3] + 32*x^2*Log[3]^2 + E^x*(2*x^3 + 16*x^2*Log[3] + 32*x*Log[3]^2)*Log[x^2] + (-4*x^3 - 16*x^2*Log[3] + E^x*
(-4*x^2 - 16*x*Log[3])*Log[x^2])*Log[x + E^x*Log[x^2]] + (2*x^2 + 2*E^x*x*Log[x^2])*Log[x + E^x*Log[x^2]]^2))/
(x^4 + 8*x^3*Log[3] + 16*x^2*Log[3]^2 + E^x*(x^3 + 8*x^2*Log[3] + 16*x*Log[3]^2)*Log[x^2] + (-2*x^3 - 8*x^2*Lo
g[3] + E^x*(-2*x^2 - 8*x*Log[3])*Log[x^2])*Log[x + E^x*Log[x^2]] + (x^2 + E^x*x*Log[x^2])*Log[x + E^x*Log[x^2]
]^2),x]

[Out]

2*Defer[Int][E^(-x - 4*Log[3] + Log[x + E^x*Log[x^2]])^(-1), x] - 4*Defer[Int][E^(-x - 4*Log[3] + Log[x + E^x*
Log[x^2]])^(-1)/(Log[x^2]*(x + Log[81] - Log[x + E^x*Log[x^2]])^2), x] - 16*Defer[Int][E^(-x - 4*Log[3] + Log[
x + E^x*Log[x^2]])^(-1)/(x*Log[x^2]*(x + Log[81] - Log[x + E^x*Log[x^2]])^2), x] - 8*Defer[Int][E^(-x - 4*Log[
3] + Log[x + E^x*Log[x^2]])^(-1)/((x + E^x*Log[x^2])*(x + Log[81] - Log[x + E^x*Log[x^2]])^2), x] + 2*(3 + 16*
Log[3]^2 - Log[81]^2)*Defer[Int][(E^(-x - 4*Log[3] + Log[x + E^x*Log[x^2]])^(-1)*x)/((x + E^x*Log[x^2])*(x + L
og[81] - Log[x + E^x*Log[x^2]])^2), x] + 2*Defer[Int][(E^(-x - 4*Log[3] + Log[x + E^x*Log[x^2]])^(-1)*x^2)/((x
+ E^x*Log[x^2])*(x + Log[81] - Log[x + E^x*Log[x^2]])^2), x] + 16*Defer[Int][E^(-x - 4*Log[3] + Log[x + E^x*L
og[x^2]])^(-1)/(Log[x^2]*(x + E^x*Log[x^2])*(x + Log[81] - Log[x + E^x*Log[x^2]])^2), x] + 4*Defer[Int][(E^(-x
- 4*Log[3] + Log[x + E^x*Log[x^2]])^(-1)*x)/(Log[x^2]*(x + E^x*Log[x^2])*(x + Log[81] - Log[x + E^x*Log[x^2]]
)^2), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+2 x^3+2 x^4+16 x^3 \log (3)+x^2 \left (6+32 \log ^2(3)\right )+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx \\ & = \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+2 x^4+x^3 (2+16 \log (3))+x^2 \left (6+32 \log ^2(3)\right )+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx \\ & = \int \frac {2 e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (-8 e^x-4 x-2 e^x x+x^4+x^3 (1+8 \log (3))+3 x^2 \left (1+\frac {16 \log ^2(3)}{3}\right )+e^x x \log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2-2 x^2 (x+\log (81)) \log \left (x+e^x \log \left (x^2\right )\right )+x^2 \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx \\ & = 2 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (-8 e^x-4 x-2 e^x x+x^4+x^3 (1+8 \log (3))+3 x^2 \left (1+\frac {16 \log ^2(3)}{3}\right )+e^x x \log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2-2 x^2 (x+\log (81)) \log \left (x+e^x \log \left (x^2\right )\right )+x^2 \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx \\ & = 2 \int \left (\frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (8+2 x-4 \log \left (x^2\right )+x^2 \log \left (x^2\right )+3 x \left (1+\frac {1}{3} \left (16 \log ^2(3)-\log ^2(81)\right )\right ) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}+\frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (-8-2 x+x^3 \log \left (x^2\right )+2 x^2 \log (81) \log \left (x^2\right )+x \log ^2(81) \log \left (x^2\right )-2 x^2 \log \left (x^2\right ) \log \left (x+e^x \log \left (x^2\right )\right )-2 x \log (81) \log \left (x^2\right ) \log \left (x+e^x \log \left (x^2\right )\right )+x \log \left (x^2\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x \log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}\right ) \, dx \\ & = 2 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (8+2 x-4 \log \left (x^2\right )+x^2 \log \left (x^2\right )+3 x \left (1+\frac {1}{3} \left (16 \log ^2(3)-\log ^2(81)\right )\right ) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx+2 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (-8-2 x+x^3 \log \left (x^2\right )+2 x^2 \log (81) \log \left (x^2\right )+x \log ^2(81) \log \left (x^2\right )-2 x^2 \log \left (x^2\right ) \log \left (x+e^x \log \left (x^2\right )\right )-2 x \log (81) \log \left (x^2\right ) \log \left (x+e^x \log \left (x^2\right )\right )+x \log \left (x^2\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x \log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx \\ & = 2 \int e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (1-\frac {2 (4+x)}{x \log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}\right ) \, dx+2 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (2 (4+x)+\left (-4+x^2+x \left (3+16 \log ^2(3)-\log ^2(81)\right )\right ) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx \\ & = 2 \int \left (e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}-\frac {2 e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} (4+x)}{x \log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}\right ) \, dx+2 \int \left (-\frac {4 e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}+\frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x^2}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}+\frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x \left (3+16 \log ^2(3)-\log ^2(81)\right )}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}+\frac {8 e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}+\frac {2 e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}\right ) \, dx \\ & = 2 \int e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \, dx+2 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x^2}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx-4 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} (4+x)}{x \log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx+4 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx-8 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx+16 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx+\left (2 \left (3+16 \log ^2(3)-\log ^2(81)\right )\right ) \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx \\ & = 2 \int e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \, dx+2 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x^2}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx-4 \int \left (\frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}+\frac {4 e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{x \log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2}\right ) \, dx+4 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx-8 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx+16 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx+\left (2 \left (3+16 \log ^2(3)-\log ^2(81)\right )\right ) \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx \\ & = 2 \int e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \, dx+2 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x^2}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx-4 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx+4 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx-8 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx-16 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{x \log \left (x^2\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx+16 \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}}}{\log \left (x^2\right ) \left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx+\left (2 \left (3+16 \log ^2(3)-\log ^2(81)\right )\right ) \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} x}{\left (x+e^x \log \left (x^2\right )\right ) \left (x+\log (81)-\log \left (x+e^x \log \left (x^2\right )\right )\right )^2} \, dx \\ \end{align*}

Mathematica [F]

\[ \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx=\int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx \]

[In]

Integrate[(E^(-x - 4*Log[3] + Log[x + E^x*Log[x^2]])^(-1)*(E^x*(-16 - 4*x) - 8*x + 6*x^2 + 2*x^3 + 2*x^4 + 16*
x^3*Log[3] + 32*x^2*Log[3]^2 + E^x*(2*x^3 + 16*x^2*Log[3] + 32*x*Log[3]^2)*Log[x^2] + (-4*x^3 - 16*x^2*Log[3]
+ E^x*(-4*x^2 - 16*x*Log[3])*Log[x^2])*Log[x + E^x*Log[x^2]] + (2*x^2 + 2*E^x*x*Log[x^2])*Log[x + E^x*Log[x^2]
]^2))/(x^4 + 8*x^3*Log[3] + 16*x^2*Log[3]^2 + E^x*(x^3 + 8*x^2*Log[3] + 16*x*Log[3]^2)*Log[x^2] + (-2*x^3 - 8*
x^2*Log[3] + E^x*(-2*x^2 - 8*x*Log[3])*Log[x^2])*Log[x + E^x*Log[x^2]] + (x^2 + E^x*x*Log[x^2])*Log[x + E^x*Lo
g[x^2]]^2),x]

[Out]

Integrate[(E^(-x - 4*Log[3] + Log[x + E^x*Log[x^2]])^(-1)*(E^x*(-16 - 4*x) - 8*x + 6*x^2 + 2*x^3 + 2*x^4 + 16*
x^3*Log[3] + 32*x^2*Log[3]^2 + E^x*(2*x^3 + 16*x^2*Log[3] + 32*x*Log[3]^2)*Log[x^2] + (-4*x^3 - 16*x^2*Log[3]
+ E^x*(-4*x^2 - 16*x*Log[3])*Log[x^2])*Log[x + E^x*Log[x^2]] + (2*x^2 + 2*E^x*x*Log[x^2])*Log[x + E^x*Log[x^2]
]^2))/(x^4 + 8*x^3*Log[3] + 16*x^2*Log[3]^2 + E^x*(x^3 + 8*x^2*Log[3] + 16*x*Log[3]^2)*Log[x^2] + (-2*x^3 - 8*
x^2*Log[3] + E^x*(-2*x^2 - 8*x*Log[3])*Log[x^2])*Log[x + E^x*Log[x^2]] + (x^2 + E^x*x*Log[x^2])*Log[x + E^x*Lo
g[x^2]]^2), x]

Maple [C] (warning: unable to verify)

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

Time = 0.13 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.11

\[\left (2 x +8\right ) {\mathrm e}^{-\frac {1}{-\ln \left ({\mathrm e}^{x} \left (2 \ln \left (x \right )-\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) {\left (-\operatorname {csgn}\left (i x^{2}\right )+\operatorname {csgn}\left (i x \right )\right )}^{2}}{2}\right )+x \right )+4 \ln \left (3\right )+x}}\]

[In]

int(((2*x*exp(x)*ln(x^2)+2*x^2)*ln(exp(x)*ln(x^2)+x)^2+((-16*x*ln(3)-4*x^2)*exp(x)*ln(x^2)-16*x^2*ln(3)-4*x^3)
*ln(exp(x)*ln(x^2)+x)+(32*x*ln(3)^2+16*x^2*ln(3)+2*x^3)*exp(x)*ln(x^2)+(-16-4*x)*exp(x)+32*x^2*ln(3)^2+16*x^3*
ln(3)+2*x^4+2*x^3+6*x^2-8*x)*exp(1/(ln(exp(x)*ln(x^2)+x)-4*ln(3)-x))/((x*exp(x)*ln(x^2)+x^2)*ln(exp(x)*ln(x^2)
+x)^2+((-8*x*ln(3)-2*x^2)*exp(x)*ln(x^2)-8*x^2*ln(3)-2*x^3)*ln(exp(x)*ln(x^2)+x)+(16*x*ln(3)^2+8*x^2*ln(3)+x^3
)*exp(x)*ln(x^2)+16*x^2*ln(3)^2+8*x^3*ln(3)+x^4),x)

[Out]

(2*x+8)*exp(-1/(-ln(exp(x)*(2*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2)+x)+4*ln(3)+x))

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx=2 \, {\left (x + 4\right )} e^{\left (-\frac {1}{x + 4 \, \log \left (3\right ) - \log \left (e^{x} \log \left (x^{2}\right ) + x\right )}\right )} \]

[In]

integrate(((2*x*exp(x)*log(x^2)+2*x^2)*log(exp(x)*log(x^2)+x)^2+((-16*x*log(3)-4*x^2)*exp(x)*log(x^2)-16*x^2*l
og(3)-4*x^3)*log(exp(x)*log(x^2)+x)+(32*x*log(3)^2+16*x^2*log(3)+2*x^3)*exp(x)*log(x^2)+(-16-4*x)*exp(x)+32*x^
2*log(3)^2+16*x^3*log(3)+2*x^4+2*x^3+6*x^2-8*x)*exp(1/(log(exp(x)*log(x^2)+x)-4*log(3)-x))/((x*exp(x)*log(x^2)
+x^2)*log(exp(x)*log(x^2)+x)^2+((-8*x*log(3)-2*x^2)*exp(x)*log(x^2)-8*x^2*log(3)-2*x^3)*log(exp(x)*log(x^2)+x)
+(16*x*log(3)^2+8*x^2*log(3)+x^3)*exp(x)*log(x^2)+16*x^2*log(3)^2+8*x^3*log(3)+x^4),x, algorithm="fricas")

[Out]

2*(x + 4)*e^(-1/(x + 4*log(3) - log(e^x*log(x^2) + x)))

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx=\text {Timed out} \]

[In]

integrate(((2*x*exp(x)*ln(x**2)+2*x**2)*ln(exp(x)*ln(x**2)+x)**2+((-16*x*ln(3)-4*x**2)*exp(x)*ln(x**2)-16*x**2
*ln(3)-4*x**3)*ln(exp(x)*ln(x**2)+x)+(32*x*ln(3)**2+16*x**2*ln(3)+2*x**3)*exp(x)*ln(x**2)+(-16-4*x)*exp(x)+32*
x**2*ln(3)**2+16*x**3*ln(3)+2*x**4+2*x**3+6*x**2-8*x)*exp(1/(ln(exp(x)*ln(x**2)+x)-4*ln(3)-x))/((x*exp(x)*ln(x
**2)+x**2)*ln(exp(x)*ln(x**2)+x)**2+((-8*x*ln(3)-2*x**2)*exp(x)*ln(x**2)-8*x**2*ln(3)-2*x**3)*ln(exp(x)*ln(x**
2)+x)+(16*x*ln(3)**2+8*x**2*ln(3)+x**3)*exp(x)*ln(x**2)+16*x**2*ln(3)**2+8*x**3*ln(3)+x**4),x)

[Out]

Timed out

Maxima [F]

\[ \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx=\int { \frac {2 \, {\left (x^{4} + 8 \, x^{3} \log \left (3\right ) + 16 \, x^{2} \log \left (3\right )^{2} + x^{3} + {\left (x^{3} + 8 \, x^{2} \log \left (3\right ) + 16 \, x \log \left (3\right )^{2}\right )} e^{x} \log \left (x^{2}\right ) + {\left (x e^{x} \log \left (x^{2}\right ) + x^{2}\right )} \log \left (e^{x} \log \left (x^{2}\right ) + x\right )^{2} + 3 \, x^{2} - 2 \, {\left (x + 4\right )} e^{x} - 2 \, {\left (x^{3} + 4 \, x^{2} \log \left (3\right ) + {\left (x^{2} + 4 \, x \log \left (3\right )\right )} e^{x} \log \left (x^{2}\right )\right )} \log \left (e^{x} \log \left (x^{2}\right ) + x\right ) - 4 \, x\right )} e^{\left (-\frac {1}{x + 4 \, \log \left (3\right ) - \log \left (e^{x} \log \left (x^{2}\right ) + x\right )}\right )}}{x^{4} + 8 \, x^{3} \log \left (3\right ) + 16 \, x^{2} \log \left (3\right )^{2} + {\left (x^{3} + 8 \, x^{2} \log \left (3\right ) + 16 \, x \log \left (3\right )^{2}\right )} e^{x} \log \left (x^{2}\right ) + {\left (x e^{x} \log \left (x^{2}\right ) + x^{2}\right )} \log \left (e^{x} \log \left (x^{2}\right ) + x\right )^{2} - 2 \, {\left (x^{3} + 4 \, x^{2} \log \left (3\right ) + {\left (x^{2} + 4 \, x \log \left (3\right )\right )} e^{x} \log \left (x^{2}\right )\right )} \log \left (e^{x} \log \left (x^{2}\right ) + x\right )} \,d x } \]

[In]

integrate(((2*x*exp(x)*log(x^2)+2*x^2)*log(exp(x)*log(x^2)+x)^2+((-16*x*log(3)-4*x^2)*exp(x)*log(x^2)-16*x^2*l
og(3)-4*x^3)*log(exp(x)*log(x^2)+x)+(32*x*log(3)^2+16*x^2*log(3)+2*x^3)*exp(x)*log(x^2)+(-16-4*x)*exp(x)+32*x^
2*log(3)^2+16*x^3*log(3)+2*x^4+2*x^3+6*x^2-8*x)*exp(1/(log(exp(x)*log(x^2)+x)-4*log(3)-x))/((x*exp(x)*log(x^2)
+x^2)*log(exp(x)*log(x^2)+x)^2+((-8*x*log(3)-2*x^2)*exp(x)*log(x^2)-8*x^2*log(3)-2*x^3)*log(exp(x)*log(x^2)+x)
+(16*x*log(3)^2+8*x^2*log(3)+x^3)*exp(x)*log(x^2)+16*x^2*log(3)^2+8*x^3*log(3)+x^4),x, algorithm="maxima")

[Out]

2*x^4*e^(-1/(x + 4*log(3) - log(2*e^x*log(x) + x)))/(x^2 - x - 2*e^x) + 16*x^3*e^(-1/(x + 4*log(3) - log(2*e^x
*log(x) + x)))*log(3)/(x^2 - x - 2*e^x) + 32*x^2*e^(-1/(x + 4*log(3) - log(2*e^x*log(x) + x)))*log(3)^2/(x^2 -
x - 2*e^x) + 4*x^3*e^(x - 1/(x + 4*log(3) - log(2*e^x*log(x) + x)))*log(x)/(x^2 - x - 2*e^x) + 32*x^2*e^(x -
1/(x + 4*log(3) - log(2*e^x*log(x) + x)))*log(3)*log(x)/(x^2 - x - 2*e^x) + 64*x*e^(x - 1/(x + 4*log(3) - log(
2*e^x*log(x) + x)))*log(3)^2*log(x)/(x^2 - x - 2*e^x) + 2*x^3*e^(-1/(x + 4*log(3) - log(2*e^x*log(x) + x)))/(x
^2 - x - 2*e^x) + 6*x^2*e^(-1/(x + 4*log(3) - log(2*e^x*log(x) + x)))/(x^2 - x - 2*e^x) - 4*x*e^(x - 1/(x + 4*
log(3) - log(2*e^x*log(x) + x)))/(x^2 - x - 2*e^x) - 8*x*e^(-1/(x + 4*log(3) - log(2*e^x*log(x) + x)))/(x^2 -
x - 2*e^x) - 16*e^(x - 1/(x + 4*log(3) - log(2*e^x*log(x) + x)))/(x^2 - x - 2*e^x) + 2*integrate(-(2*(x + 4*lo
g(3))*log(2*e^x*log(x) + x) - log(2*e^x*log(x) + x)^2)*e^(-1/(x + 4*log(3) - log(2*e^x*log(x) + x)))/(x^2 + 8*
x*log(3) + 16*log(3)^2 - 2*(x + 4*log(3))*log(2*e^x*log(x) + x) + log(2*e^x*log(x) + x)^2), x)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (28) = 56\).

Time = 3.42 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.86 \[ \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx=2 \, x e^{\left (\frac {x - \log \left (e^{x} \log \left (x^{2}\right ) + x\right )}{4 \, {\left (x \log \left (3\right ) + 4 \, \log \left (3\right )^{2} - \log \left (3\right ) \log \left (e^{x} \log \left (x^{2}\right ) + x\right )\right )}} - \frac {1}{4 \, \log \left (3\right )}\right )} + 8 \, e^{\left (\frac {x - \log \left (e^{x} \log \left (x^{2}\right ) + x\right )}{4 \, {\left (x \log \left (3\right ) + 4 \, \log \left (3\right )^{2} - \log \left (3\right ) \log \left (e^{x} \log \left (x^{2}\right ) + x\right )\right )}} - \frac {1}{4 \, \log \left (3\right )}\right )} \]

[In]

integrate(((2*x*exp(x)*log(x^2)+2*x^2)*log(exp(x)*log(x^2)+x)^2+((-16*x*log(3)-4*x^2)*exp(x)*log(x^2)-16*x^2*l
og(3)-4*x^3)*log(exp(x)*log(x^2)+x)+(32*x*log(3)^2+16*x^2*log(3)+2*x^3)*exp(x)*log(x^2)+(-16-4*x)*exp(x)+32*x^
2*log(3)^2+16*x^3*log(3)+2*x^4+2*x^3+6*x^2-8*x)*exp(1/(log(exp(x)*log(x^2)+x)-4*log(3)-x))/((x*exp(x)*log(x^2)
+x^2)*log(exp(x)*log(x^2)+x)^2+((-8*x*log(3)-2*x^2)*exp(x)*log(x^2)-8*x^2*log(3)-2*x^3)*log(exp(x)*log(x^2)+x)
+(16*x*log(3)^2+8*x^2*log(3)+x^3)*exp(x)*log(x^2)+16*x^2*log(3)^2+8*x^3*log(3)+x^4),x, algorithm="giac")

[Out]

2*x*e^(1/4*(x - log(e^x*log(x^2) + x))/(x*log(3) + 4*log(3)^2 - log(3)*log(e^x*log(x^2) + x)) - 1/4/log(3)) +
8*e^(1/4*(x - log(e^x*log(x^2) + x))/(x*log(3) + 4*log(3)^2 - log(3)*log(e^x*log(x^2) + x)) - 1/4/log(3))

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{\frac {1}{-x-4 \log (3)+\log \left (x+e^x \log \left (x^2\right )\right )}} \left (e^x (-16-4 x)-8 x+6 x^2+2 x^3+2 x^4+16 x^3 \log (3)+32 x^2 \log ^2(3)+e^x \left (2 x^3+16 x^2 \log (3)+32 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-4 x^3-16 x^2 \log (3)+e^x \left (-4 x^2-16 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (2 x^2+2 e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )\right )}{x^4+8 x^3 \log (3)+16 x^2 \log ^2(3)+e^x \left (x^3+8 x^2 \log (3)+16 x \log ^2(3)\right ) \log \left (x^2\right )+\left (-2 x^3-8 x^2 \log (3)+e^x \left (-2 x^2-8 x \log (3)\right ) \log \left (x^2\right )\right ) \log \left (x+e^x \log \left (x^2\right )\right )+\left (x^2+e^x x \log \left (x^2\right )\right ) \log ^2\left (x+e^x \log \left (x^2\right )\right )} \, dx=\int \frac {{\mathrm {e}}^{-\frac {1}{x+4\,\ln \left (3\right )-\ln \left (x+\ln \left (x^2\right )\,{\mathrm {e}}^x\right )}}\,\left (32\,x^2\,{\ln \left (3\right )}^2-8\,x+{\ln \left (x+\ln \left (x^2\right )\,{\mathrm {e}}^x\right )}^2\,\left (2\,x^2+2\,x\,\ln \left (x^2\right )\,{\mathrm {e}}^x\right )-{\mathrm {e}}^x\,\left (4\,x+16\right )+16\,x^3\,\ln \left (3\right )-\ln \left (x+\ln \left (x^2\right )\,{\mathrm {e}}^x\right )\,\left (16\,x^2\,\ln \left (3\right )+4\,x^3+\ln \left (x^2\right )\,{\mathrm {e}}^x\,\left (4\,x^2+16\,\ln \left (3\right )\,x\right )\right )+6\,x^2+2\,x^3+2\,x^4+\ln \left (x^2\right )\,{\mathrm {e}}^x\,\left (2\,x^3+16\,\ln \left (3\right )\,x^2+32\,{\ln \left (3\right )}^2\,x\right )\right )}{16\,x^2\,{\ln \left (3\right )}^2+8\,x^3\,\ln \left (3\right )+{\ln \left (x+\ln \left (x^2\right )\,{\mathrm {e}}^x\right )}^2\,\left (x^2+x\,\ln \left (x^2\right )\,{\mathrm {e}}^x\right )-\ln \left (x+\ln \left (x^2\right )\,{\mathrm {e}}^x\right )\,\left (8\,x^2\,\ln \left (3\right )+2\,x^3+\ln \left (x^2\right )\,{\mathrm {e}}^x\,\left (2\,x^2+8\,\ln \left (3\right )\,x\right )\right )+x^4+\ln \left (x^2\right )\,{\mathrm {e}}^x\,\left (x^3+8\,\ln \left (3\right )\,x^2+16\,{\ln \left (3\right )}^2\,x\right )} \,d x \]

[In]

int((exp(-1/(x + 4*log(3) - log(x + log(x^2)*exp(x))))*(32*x^2*log(3)^2 - 8*x + log(x + log(x^2)*exp(x))^2*(2*
x^2 + 2*x*log(x^2)*exp(x)) - exp(x)*(4*x + 16) + 16*x^3*log(3) - log(x + log(x^2)*exp(x))*(16*x^2*log(3) + 4*x
^3 + log(x^2)*exp(x)*(16*x*log(3) + 4*x^2)) + 6*x^2 + 2*x^3 + 2*x^4 + log(x^2)*exp(x)*(32*x*log(3)^2 + 16*x^2*
log(3) + 2*x^3)))/(16*x^2*log(3)^2 + 8*x^3*log(3) + log(x + log(x^2)*exp(x))^2*(x^2 + x*log(x^2)*exp(x)) - log
(x + log(x^2)*exp(x))*(8*x^2*log(3) + 2*x^3 + log(x^2)*exp(x)*(8*x*log(3) + 2*x^2)) + x^4 + log(x^2)*exp(x)*(1
6*x*log(3)^2 + 8*x^2*log(3) + x^3)),x)

[Out]

int((exp(-1/(x + 4*log(3) - log(x + log(x^2)*exp(x))))*(32*x^2*log(3)^2 - 8*x + log(x + log(x^2)*exp(x))^2*(2*
x^2 + 2*x*log(x^2)*exp(x)) - exp(x)*(4*x + 16) + 16*x^3*log(3) - log(x + log(x^2)*exp(x))*(16*x^2*log(3) + 4*x
^3 + log(x^2)*exp(x)*(16*x*log(3) + 4*x^2)) + 6*x^2 + 2*x^3 + 2*x^4 + log(x^2)*exp(x)*(32*x*log(3)^2 + 16*x^2*
log(3) + 2*x^3)))/(16*x^2*log(3)^2 + 8*x^3*log(3) + log(x + log(x^2)*exp(x))^2*(x^2 + x*log(x^2)*exp(x)) - log
(x + log(x^2)*exp(x))*(8*x^2*log(3) + 2*x^3 + log(x^2)*exp(x)*(8*x*log(3) + 2*x^2)) + x^4 + log(x^2)*exp(x)*(1
6*x*log(3)^2 + 8*x^2*log(3) + x^3)), x)