\[ \int \frac {\left (-2 x^2-8 e^x x^2\right ) \log ^2(x)+\left (\left (-2 x^2+8 e^x x^3\right ) \log (x)+\left (-2 x^2+8 e^x x^3\right ) \log ^2(x)\right ) \log \left (e^{-x} \left (-2+8 e^x x\right )\right )+\left (\left (2 x+8 e^x x\right ) \log ^2(x)+\left (\left (4 x-16 e^x x^2\right ) \log (x)+\left (2 x-8 e^x x^2\right ) \log ^2(x)\right ) \log \left (e^{-x} \left (-2+8 e^x x\right )\right )\right ) \log \left (\log \left (e^{-x} \left (-2+8 e^x x\right )\right )\right )+\left (-2+8 e^x x\right ) \log (x) \log \left (e^{-x} \left (-2+8 e^x x\right )\right ) \log ^2\left (\log \left (e^{-x} \left (-2+8 e^x x\right )\right )\right )}{\left (-x+4 e^x x^2\right ) \log \left (e^{-x} \left (-2+8 e^x x\right )\right )} \, dx \]
Optimal antiderivative \[ \left (x -\ln \! \left (\ln \! \left (8 x -2 \,{\mathrm e}^{-x}\right )\right )\right )^{2} \ln \! \left (x \right )^{2} \]
command
integrate(((8*exp(x)*x-2)*log(x)*log((8*exp(x)*x-2)/exp(x))*log(log((8*exp(x)*x-2)/exp(x)))^2+(((-8*exp(x)*x^2+2*x)*log(x)^2+(-16*exp(x)*x^2+4*x)*log(x))*log((8*exp(x)*x-2)/exp(x))+(8*exp(x)*x+2*x)*log(x)^2)*log(log((8*exp(x)*x-2)/exp(x)))+((8*exp(x)*x^3-2*x^2)*log(x)^2+(8*exp(x)*x^3-2*x^2)*log(x))*log((8*exp(x)*x-2)/exp(x))+(-8*exp(x)*x^2-2*x^2)*log(x)^2)/(4*exp(x)*x^2-x)/log((8*exp(x)*x-2)/exp(x)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Timed out} \]
Giac 1.7.0 via sagemath 9.3 output
\[ x^{2} \log \left (x\right )^{2} - 2 \, x \log \left (x\right )^{2} \log \left (-x + \log \left (2\right ) + \log \left (4 \, x e^{x} - 1\right )\right ) + \log \left (x\right )^{2} \log \left (-x + \log \left (2\right ) + \log \left (4 \, x e^{x} - 1\right )\right )^{2} \]