\[ \int \frac {e^{-4+x} (-4+4 x)+\left (-36 e^{-3+x}+4 x\right ) \log ^2\left (e^{3-x} \left (-9 e^{-3+x}+x\right )\right )}{\left (9 e^{-7+2 x}-e^{-4+x} x\right ) \log ^2\left (e^{3-x} \left (-9 e^{-3+x}+x\right )\right )} \, dx \]
Optimal antiderivative \[ 4 \,{\mathrm e}^{-x +4}-\frac {4}{\ln \! \left (x \,{\mathrm e}^{-x +3}-9\right )} \]
command
Int[(E^(-4 + x)*(-4 + 4*x) + (-36*E^(-3 + x) + 4*x)*Log[E^(3 - x)*(-9*E^(-3 + x) + x)]^2)/((9*E^(-7 + 2*x) - E^(-4 + x)*x)*Log[E^(3 - x)*(-9*E^(-3 + x) + x)]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{-4+x} (-4+4 x)+\left (-36 e^{-3+x}+4 x\right ) \log ^2\left (e^{3-x} \left (-9 e^{-3+x}+x\right )\right )}{\left (9 e^{-7+2 x}-e^{-4+x} x\right ) \log ^2\left (e^{3-x} \left (-9 e^{-3+x}+x\right )\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ 4 e^{4-x}-\frac {4}{\log \left (e^{3-x} x-9\right )} \]