\[ \int \frac {4 e^x x+\left (10-2 e^4-2 e^x\right ) \log \left (\frac {4 \left (5-e^4-e^x\right )^2}{e^{10}}\right )}{\left (-5 x+e^4 x+e^x x\right ) \log \left (\frac {4 \left (5-e^4-e^x\right )^2}{e^{10}}\right )} \, dx \]
Optimal antiderivative \[ 2 \ln \! \left (\frac {3 \ln \! \left (4 \left (-{\mathrm e}^{x}+5-{\mathrm e}^{4}\right )^{2} {\mathrm e}^{-10}\right )}{x}\right ) \]
command
Int[(4*E^x*x + (10 - 2*E^4 - 2*E^x)*Log[(4*(5 - E^4 - E^x)^2)/E^10])/((-5*x + E^4*x + E^x*x)*Log[(4*(5 - E^4 - E^x)^2)/E^10]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {4 e^x x+\left (10-2 e^4-2 e^x\right ) \log \left (\frac {4 \left (5-e^4-e^x\right )^2}{e^{10}}\right )}{\left (-5 x+e^4 x+e^x x\right ) \log \left (\frac {4 \left (5-e^4-e^x\right )^2}{e^{10}}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ 2 \log \left (-\log \left (\left (e^x-5+e^4\right )^2\right )+10-\log (4)\right )-2 \log (x) \]