\[ \int \frac {e^{-4+e^x} (16-16 x)+e^{-4+e^x} \left (e^x \left (16 x-16 x^2\right )+4 e^x x \log \left (-x^4\right )\right ) \log \left (4-4 x+\log \left (-x^4\right )\right )}{4 x-4 x^2+x \log \left (-x^4\right )} \, dx \]
Optimal antiderivative \[ 4 \,{\mathrm e}^{{\mathrm e}^{x}-4} \ln \! \left (\ln \! \left (-x^{4}\right )-4 x +4\right ) \]
command
Int[(E^(-4 + E^x)*(16 - 16*x) + E^(-4 + E^x)*(E^x*(16*x - 16*x^2) + 4*E^x*x*Log[-x^4])*Log[4 - 4*x + Log[-x^4]])/(4*x - 4*x^2 + x*Log[-x^4]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{-4+e^x} (16-16 x)+e^{-4+e^x} \left (e^x \left (16 x-16 x^2\right )+4 e^x x \log \left (-x^4\right )\right ) \log \left (4-4 x+\log \left (-x^4\right )\right )}{4 x-4 x^2+x \log \left (-x^4\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ 4 e^{e^x-4} \log \left (\log \left (-x^4\right )-4 x+4\right ) \]