Integrand size = 247, antiderivative size = 28 \[ \int \frac {e^{e^{8 e^x}+2 e^{4 e^x} \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )+\log ^2\left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )} x \left (e^{4 e^x} \left (8+2 e^x x^2\right )+\left (-4+2 x+e^x x+e^{8 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )+\left (8+2 e^x x^2+e^{4 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )\right ) \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )\right )}{\left (-4 x+2 x^2+e^x x^2\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )} \, dx=e^{\left (e^{4 e^x}+\log \left (\log \left (-2-e^x+\frac {4}{x}\right )\right )\right )^2} x \]
Time = 0.32 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.82 \[ \int \frac {e^{e^{8 e^x}+2 e^{4 e^x} \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )+\log ^2\left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )} x \left (e^{4 e^x} \left (8+2 e^x x^2\right )+\left (-4+2 x+e^x x+e^{8 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )+\left (8+2 e^x x^2+e^{4 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )\right ) \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )\right )}{\left (-4 x+2 x^2+e^x x^2\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )} \, dx=e^{e^{8 e^x}+\log ^2\left (\log \left (-2-e^x+\frac {4}{x}\right )\right )} x \log ^{2 e^{4 e^x}}\left (-2-e^x+\frac {4}{x}\right ) \]
Integrate[(E^(E^(8*E^x) + 2*E^(4*E^x)*Log[Log[(4 - 2*x - E^x*x)/x]] + Log[ Log[(4 - 2*x - E^x*x)/x]]^2)*x*(E^(4*E^x)*(8 + 2*E^x*x^2) + (-4 + 2*x + E^ x*x + E^(8*E^x)*(8*E^(2*x)*x^2 + E^x*(-32*x + 16*x^2)))*Log[(4 - 2*x - E^x *x)/x] + (8 + 2*E^x*x^2 + E^(4*E^x)*(8*E^(2*x)*x^2 + E^x*(-32*x + 16*x^2)) *Log[(4 - 2*x - E^x*x)/x])*Log[Log[(4 - 2*x - E^x*x)/x]]))/((-4*x + 2*x^2 + E^x*x^2)*Log[(4 - 2*x - E^x*x)/x]),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {x \left (e^{4 e^x} \left (2 e^x x^2+8\right )+\left (e^{8 e^x} \left (8 e^{2 x} x^2+e^x \left (16 x^2-32 x\right )\right )+e^x x+2 x-4\right ) \log \left (\frac {-e^x x-2 x+4}{x}\right )+\left (2 e^x x^2+e^{4 e^x} \left (8 e^{2 x} x^2+e^x \left (16 x^2-32 x\right )\right ) \log \left (\frac {-e^x x-2 x+4}{x}\right )+8\right ) \log \left (\log \left (\frac {-e^x x-2 x+4}{x}\right )\right )\right ) \exp \left (e^{8 e^x}+\log ^2\left (\log \left (\frac {-e^x x-2 x+4}{x}\right )\right )+2 e^{4 e^x} \log \left (\log \left (\frac {-e^x x-2 x+4}{x}\right )\right )\right )}{\left (e^x x^2+2 x^2-4 x\right ) \log \left (\frac {-e^x x-2 x+4}{x}\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {x e^{\left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right )^2} \left (-e^{4 e^x} \left (2 e^x x^2+8\right )-\left (e^{8 e^x} \left (8 e^{2 x} x^2+e^x \left (16 x^2-32 x\right )\right )+e^x x+2 x-4\right ) \log \left (\frac {-e^x x-2 x+4}{x}\right )-\left (2 e^x x^2+e^{4 e^x} \left (8 e^{2 x} x^2+e^x \left (16 x^2-32 x\right )\right ) \log \left (\frac {-e^x x-2 x+4}{x}\right )+8\right ) \log \left (\log \left (\frac {-e^x x-2 x+4}{x}\right )\right )\right )}{\left (-e^x x^2-2 x^2+4 x\right ) \log \left (-e^x+\frac {4}{x}-2\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (8 x \left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right ) \exp \left (4 e^x+x+\left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right )^2\right )-\frac {4 \left (x^2-2 x-2\right ) e^{\left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right )^2} \left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right )}{\left (e^x x+2 x-4\right ) \log \left (-e^x+\frac {4}{x}-2\right )}+\frac {e^{\left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right )^2} \left (2 e^{4 e^x} x+2 x \log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )+\log \left (-e^x+\frac {4}{x}-2\right )\right )}{\log \left (-e^x+\frac {4}{x}-2\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (8 x \left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right ) \exp \left (4 e^x+x+\left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right )^2\right )-\frac {4 \left (x^2-2 x-2\right ) e^{\left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right )^2} \left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right )}{\left (e^x x+2 x-4\right ) \log \left (-e^x+\frac {4}{x}-2\right )}+\frac {e^{\left (e^{4 e^x}+\log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )\right )^2} \left (2 e^{4 e^x} x+2 x \log \left (\log \left (-e^x+\frac {4}{x}-2\right )\right )+\log \left (-e^x+\frac {4}{x}-2\right )\right )}{\log \left (-e^x+\frac {4}{x}-2\right )}\right )dx\) |
Int[(E^(E^(8*E^x) + 2*E^(4*E^x)*Log[Log[(4 - 2*x - E^x*x)/x]] + Log[Log[(4 - 2*x - E^x*x)/x]]^2)*x*(E^(4*E^x)*(8 + 2*E^x*x^2) + (-4 + 2*x + E^x*x + E^(8*E^x)*(8*E^(2*x)*x^2 + E^x*(-32*x + 16*x^2)))*Log[(4 - 2*x - E^x*x)/x] + (8 + 2*E^x*x^2 + E^(4*E^x)*(8*E^(2*x)*x^2 + E^x*(-32*x + 16*x^2))*Log[( 4 - 2*x - E^x*x)/x])*Log[Log[(4 - 2*x - E^x*x)/x]]))/((-4*x + 2*x^2 + E^x* x^2)*Log[(4 - 2*x - E^x*x)/x]),x]
3.3.20.3.1 Defintions of rubi rules used
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.13 (sec) , antiderivative size = 281, normalized size of antiderivative = 10.04
\[{\left (i \pi -\ln \left (x \right )+\ln \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right ) \left (-\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right )+\operatorname {csgn}\left (\frac {i}{x}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right )+\operatorname {csgn}\left (i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )\right )\right )}{2}+i \pi {\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right )}^{2} \left (\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right )-1\right )\right )}^{2 \,{\mathrm e}^{4 \,{\mathrm e}^{x}}} x \,{\mathrm e}^{{\ln \left (i \pi -\ln \left (x \right )+\ln \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right ) \left (-\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right )+\operatorname {csgn}\left (\frac {i}{x}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right )+\operatorname {csgn}\left (i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )\right )\right )}{2}+i \pi {\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right )}^{2} \left (\operatorname {csgn}\left (\frac {i \left (-4+\left ({\mathrm e}^{x}+2\right ) x \right )}{x}\right )-1\right )\right )}^{2}+{\mathrm e}^{8 \,{\mathrm e}^{x}}}\]
int((((8*exp(x)^2*x^2+(16*x^2-32*x)*exp(x))*exp(4*exp(x))*ln((-exp(x)*x+4- 2*x)/x)+2*exp(x)*x^2+8)*ln(ln((-exp(x)*x+4-2*x)/x))+((8*exp(x)^2*x^2+(16*x ^2-32*x)*exp(x))*exp(4*exp(x))^2+exp(x)*x+2*x-4)*ln((-exp(x)*x+4-2*x)/x)+( 2*exp(x)*x^2+8)*exp(4*exp(x)))*exp(ln(ln((-exp(x)*x+4-2*x)/x))^2+2*exp(4*e xp(x))*ln(ln((-exp(x)*x+4-2*x)/x))+exp(4*exp(x))^2+ln(x))/(exp(x)*x^2+2*x^ 2-4*x)/ln((-exp(x)*x+4-2*x)/x),x)
(I*Pi-ln(x)+ln(-4+(exp(x)+2)*x)-1/2*I*Pi*csgn(I/x*(-4+(exp(x)+2)*x))*(-csg n(I/x*(-4+(exp(x)+2)*x))+csgn(I/x))*(-csgn(I/x*(-4+(exp(x)+2)*x))+csgn(I*( -4+(exp(x)+2)*x)))+I*Pi*csgn(I/x*(-4+(exp(x)+2)*x))^2*(csgn(I/x*(-4+(exp(x )+2)*x))-1))^(2*exp(4*exp(x)))*x*exp(ln(I*Pi-ln(x)+ln(-4+(exp(x)+2)*x)-1/2 *I*Pi*csgn(I/x*(-4+(exp(x)+2)*x))*(-csgn(I/x*(-4+(exp(x)+2)*x))+csgn(I/x)) *(-csgn(I/x*(-4+(exp(x)+2)*x))+csgn(I*(-4+(exp(x)+2)*x)))+I*Pi*csgn(I/x*(- 4+(exp(x)+2)*x))^2*(csgn(I/x*(-4+(exp(x)+2)*x))-1))^2+exp(8*exp(x)))
Time = 0.25 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.79 \[ \int \frac {e^{e^{8 e^x}+2 e^{4 e^x} \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )+\log ^2\left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )} x \left (e^{4 e^x} \left (8+2 e^x x^2\right )+\left (-4+2 x+e^x x+e^{8 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )+\left (8+2 e^x x^2+e^{4 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )\right ) \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )\right )}{\left (-4 x+2 x^2+e^x x^2\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )} \, dx=e^{\left (2 \, e^{\left (4 \, e^{x}\right )} \log \left (\log \left (-\frac {x e^{x} + 2 \, x - 4}{x}\right )\right ) + \log \left (\log \left (-\frac {x e^{x} + 2 \, x - 4}{x}\right )\right )^{2} + e^{\left (8 \, e^{x}\right )} + \log \left (x\right )\right )} \]
integrate((((8*exp(x)^2*x^2+(16*x^2-32*x)*exp(x))*exp(4*exp(x))*log((-exp( x)*x+4-2*x)/x)+2*exp(x)*x^2+8)*log(log((-exp(x)*x+4-2*x)/x))+((8*exp(x)^2* x^2+(16*x^2-32*x)*exp(x))*exp(4*exp(x))^2+exp(x)*x+2*x-4)*log((-exp(x)*x+4 -2*x)/x)+(2*exp(x)*x^2+8)*exp(4*exp(x)))*exp(log(log((-exp(x)*x+4-2*x)/x)) ^2+2*exp(4*exp(x))*log(log((-exp(x)*x+4-2*x)/x))+exp(4*exp(x))^2+log(x))/( exp(x)*x^2+2*x^2-4*x)/log((-exp(x)*x+4-2*x)/x),x, algorithm=\
e^(2*e^(4*e^x)*log(log(-(x*e^x + 2*x - 4)/x)) + log(log(-(x*e^x + 2*x - 4) /x))^2 + e^(8*e^x) + log(x))
Timed out. \[ \int \frac {e^{e^{8 e^x}+2 e^{4 e^x} \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )+\log ^2\left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )} x \left (e^{4 e^x} \left (8+2 e^x x^2\right )+\left (-4+2 x+e^x x+e^{8 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )+\left (8+2 e^x x^2+e^{4 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )\right ) \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )\right )}{\left (-4 x+2 x^2+e^x x^2\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )} \, dx=\text {Timed out} \]
integrate((((8*exp(x)**2*x**2+(16*x**2-32*x)*exp(x))*exp(4*exp(x))*ln((-ex p(x)*x+4-2*x)/x)+2*exp(x)*x**2+8)*ln(ln((-exp(x)*x+4-2*x)/x))+((8*exp(x)** 2*x**2+(16*x**2-32*x)*exp(x))*exp(4*exp(x))**2+exp(x)*x+2*x-4)*ln((-exp(x) *x+4-2*x)/x)+(2*exp(x)*x**2+8)*exp(4*exp(x)))*exp(ln(ln((-exp(x)*x+4-2*x)/ x))**2+2*exp(4*exp(x))*ln(ln((-exp(x)*x+4-2*x)/x))+exp(4*exp(x))**2+ln(x)) /(exp(x)*x**2+2*x**2-4*x)/ln((-exp(x)*x+4-2*x)/x),x)
Leaf count of result is larger than twice the leaf count of optimal. 52 vs. \(2 (25) = 50\).
Time = 0.68 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86 \[ \int \frac {e^{e^{8 e^x}+2 e^{4 e^x} \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )+\log ^2\left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )} x \left (e^{4 e^x} \left (8+2 e^x x^2\right )+\left (-4+2 x+e^x x+e^{8 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )+\left (8+2 e^x x^2+e^{4 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )\right ) \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )\right )}{\left (-4 x+2 x^2+e^x x^2\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )} \, dx=x e^{\left (2 \, e^{\left (4 \, e^{x}\right )} \log \left (\log \left (-x e^{x} - 2 \, x + 4\right ) - \log \left (x\right )\right ) + \log \left (\log \left (-x e^{x} - 2 \, x + 4\right ) - \log \left (x\right )\right )^{2} + e^{\left (8 \, e^{x}\right )}\right )} \]
integrate((((8*exp(x)^2*x^2+(16*x^2-32*x)*exp(x))*exp(4*exp(x))*log((-exp( x)*x+4-2*x)/x)+2*exp(x)*x^2+8)*log(log((-exp(x)*x+4-2*x)/x))+((8*exp(x)^2* x^2+(16*x^2-32*x)*exp(x))*exp(4*exp(x))^2+exp(x)*x+2*x-4)*log((-exp(x)*x+4 -2*x)/x)+(2*exp(x)*x^2+8)*exp(4*exp(x)))*exp(log(log((-exp(x)*x+4-2*x)/x)) ^2+2*exp(4*exp(x))*log(log((-exp(x)*x+4-2*x)/x))+exp(4*exp(x))^2+log(x))/( exp(x)*x^2+2*x^2-4*x)/log((-exp(x)*x+4-2*x)/x),x, algorithm=\
x*e^(2*e^(4*e^x)*log(log(-x*e^x - 2*x + 4) - log(x)) + log(log(-x*e^x - 2* x + 4) - log(x))^2 + e^(8*e^x))
\[ \int \frac {e^{e^{8 e^x}+2 e^{4 e^x} \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )+\log ^2\left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )} x \left (e^{4 e^x} \left (8+2 e^x x^2\right )+\left (-4+2 x+e^x x+e^{8 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )+\left (8+2 e^x x^2+e^{4 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )\right ) \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )\right )}{\left (-4 x+2 x^2+e^x x^2\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )} \, dx=\int { \frac {{\left (2 \, {\left (x^{2} e^{x} + 4\right )} e^{\left (4 \, e^{x}\right )} + {\left (x e^{x} + 8 \, {\left (x^{2} e^{\left (2 \, x\right )} + 2 \, {\left (x^{2} - 2 \, x\right )} e^{x}\right )} e^{\left (8 \, e^{x}\right )} + 2 \, x - 4\right )} \log \left (-\frac {x e^{x} + 2 \, x - 4}{x}\right ) + 2 \, {\left (x^{2} e^{x} + 4 \, {\left (x^{2} e^{\left (2 \, x\right )} + 2 \, {\left (x^{2} - 2 \, x\right )} e^{x}\right )} e^{\left (4 \, e^{x}\right )} \log \left (-\frac {x e^{x} + 2 \, x - 4}{x}\right ) + 4\right )} \log \left (\log \left (-\frac {x e^{x} + 2 \, x - 4}{x}\right )\right )\right )} e^{\left (2 \, e^{\left (4 \, e^{x}\right )} \log \left (\log \left (-\frac {x e^{x} + 2 \, x - 4}{x}\right )\right ) + \log \left (\log \left (-\frac {x e^{x} + 2 \, x - 4}{x}\right )\right )^{2} + e^{\left (8 \, e^{x}\right )} + \log \left (x\right )\right )}}{{\left (x^{2} e^{x} + 2 \, x^{2} - 4 \, x\right )} \log \left (-\frac {x e^{x} + 2 \, x - 4}{x}\right )} \,d x } \]
integrate((((8*exp(x)^2*x^2+(16*x^2-32*x)*exp(x))*exp(4*exp(x))*log((-exp( x)*x+4-2*x)/x)+2*exp(x)*x^2+8)*log(log((-exp(x)*x+4-2*x)/x))+((8*exp(x)^2* x^2+(16*x^2-32*x)*exp(x))*exp(4*exp(x))^2+exp(x)*x+2*x-4)*log((-exp(x)*x+4 -2*x)/x)+(2*exp(x)*x^2+8)*exp(4*exp(x)))*exp(log(log((-exp(x)*x+4-2*x)/x)) ^2+2*exp(4*exp(x))*log(log((-exp(x)*x+4-2*x)/x))+exp(4*exp(x))^2+log(x))/( exp(x)*x^2+2*x^2-4*x)/log((-exp(x)*x+4-2*x)/x),x, algorithm=\
Time = 8.43 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.79 \[ \int \frac {e^{e^{8 e^x}+2 e^{4 e^x} \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )+\log ^2\left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )} x \left (e^{4 e^x} \left (8+2 e^x x^2\right )+\left (-4+2 x+e^x x+e^{8 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )+\left (8+2 e^x x^2+e^{4 e^x} \left (8 e^{2 x} x^2+e^x \left (-32 x+16 x^2\right )\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )\right ) \log \left (\log \left (\frac {4-2 x-e^x x}{x}\right )\right )\right )}{\left (-4 x+2 x^2+e^x x^2\right ) \log \left (\frac {4-2 x-e^x x}{x}\right )} \, dx=x\,{\mathrm {e}}^{{\mathrm {e}}^{8\,{\mathrm {e}}^x}}\,{\mathrm {e}}^{{\ln \left (\ln \left (-\frac {2\,x+x\,{\mathrm {e}}^x-4}{x}\right )\right )}^2}\,{\ln \left (-\frac {2\,x+x\,{\mathrm {e}}^x-4}{x}\right )}^{2\,{\mathrm {e}}^{4\,{\mathrm {e}}^x}} \]
int((exp(exp(8*exp(x)) + log(x) + log(log(-(2*x + x*exp(x) - 4)/x))^2 + 2* exp(4*exp(x))*log(log(-(2*x + x*exp(x) - 4)/x)))*(log(-(2*x + x*exp(x) - 4 )/x)*(2*x + exp(8*exp(x))*(8*x^2*exp(2*x) - exp(x)*(32*x - 16*x^2)) + x*ex p(x) - 4) + exp(4*exp(x))*(2*x^2*exp(x) + 8) + log(log(-(2*x + x*exp(x) - 4)/x))*(2*x^2*exp(x) + exp(4*exp(x))*log(-(2*x + x*exp(x) - 4)/x)*(8*x^2*e xp(2*x) - exp(x)*(32*x - 16*x^2)) + 8)))/(log(-(2*x + x*exp(x) - 4)/x)*(x^ 2*exp(x) - 4*x + 2*x^2)),x)