\[ \int \frac {e^3 (-1-x) \left (e^{-1+x} \left (-3 e^{1-x}+x\right )\right )^{e^3}}{3 e^{1-x}-x} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{{\mathrm e}^{3} \ln \left (x \,{\mathrm e}^{-1+x}-3\right )} \]
command
Int[(E^3*(-1 - x)*(E^(-1 + x)*(-3*E^(1 - x) + x))^E^3)/(3*E^(1 - x) - x),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^3 (-1-x) \left (e^{-1+x} \left (-3 e^{1-x}+x\right )\right )^{e^3}}{3 e^{1-x}-x} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{-e^3} \left (e^x x-3 e\right )^{e^3} \]