\[ \int \frac {e^{32-x} \left (e^x (2-9 x)+e^4 (-2+x)\right ) x}{\left (-3 e^4+3 e^x\right ) \left (e^8+e^{2 x}-2 e^{4+x}\right )^4} \, dx \]
Optimal antiderivative \[ \frac {x^{2} {\mathrm e}^{-x}}{3 \left ({\mathrm e}^{x -4}-1\right )^{8}} \]
command
Int[(E^(32 - x)*(E^x*(2 - 9*x) + E^4*(-2 + x))*x)/((-3*E^4 + 3*E^x)*(E^8 + E^(2*x) - 2*E^(4 + x))^4),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{32-x} \left (e^x (2-9 x)+e^4 (-2+x)\right ) x}{\left (-3 e^4+3 e^x\right ) \left (e^8+e^{2 x}-2 e^{4+x}\right )^4} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {1}{3} e^{-x} x^2+\frac {x^2}{3 \left (e^4-e^x\right )}+\frac {e^4 x^2}{3 \left (e^4-e^x\right )^2}+\frac {e^8 x^2}{3 \left (e^4-e^x\right )^3}+\frac {e^{12} x^2}{3 \left (e^4-e^x\right )^4}+\frac {e^{16} x^2}{3 \left (e^4-e^x\right )^5}+\frac {e^{20} x^2}{3 \left (e^4-e^x\right )^6}+\frac {e^{24} x^2}{3 \left (e^4-e^x\right )^7}+\frac {e^{28} x^2}{3 \left (e^4-e^x\right )^8} \]