\[ \int \frac {e^{e^{-4+4 x^2}} \left (-8+8 x-2 x^2+e^{-4+4 x^2} \left (64 x^2-64 x^3+16 x^4\right )\right )+x^2 \log (3)}{8 x^2-8 x^3+2 x^4} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (3\right )}{4-2 x}+\frac {{\mathrm e}^{{\mathrm e}^{4 x^{2}-4}}}{x} \]
command
Int[(E^E^(-4 + 4*x^2)*(-8 + 8*x - 2*x^2 + E^(-4 + 4*x^2)*(64*x^2 - 64*x^3 + 16*x^4)) + x^2*Log[3])/(8*x^2 - 8*x^3 + 2*x^4),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{e^{-4+4 x^2}} \left (-8+8 x-2 x^2+e^{-4+4 x^2} \left (64 x^2-64 x^3+16 x^4\right )\right )+x^2 \log (3)}{8 x^2-8 x^3+2 x^4} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {e^{e^{4 x^2-4}}}{x}+\frac {\log (3)}{2 (2-x)} \]