\[ \int \frac {-36+e^{x+x^2 \log (3 x)} \left (-16+16 x+16 x^2+32 x^2 \log (3 x)\right )}{81+16 e^{2 x+2 x^2 \log (3 x)}+e^{x+x^2 \log (3 x)} (72-32 x)-72 x+16 x^2} \, dx \]
Optimal antiderivative \[ \frac {x}{x -\frac {9}{4}-{\mathrm e}^{x^{2} \ln \left (3 x \right )+x}} \]
command
Integrate[(-36 + E^(x + x^2*Log[3*x])*(-16 + 16*x + 16*x^2 + 32*x^2*Log[3*x]))/(81 + 16*E^(2*x + 2*x^2*Log[3*x]) + E^(x + x^2*Log[3*x])*(72 - 32*x) - 72*x + 16*x^2),x]
Mathematica 13.1 output
\[ \int \frac {-36+e^{x+x^2 \log (3 x)} \left (-16+16 x+16 x^2+32 x^2 \log (3 x)\right )}{81+16 e^{2 x+2 x^2 \log (3 x)}+e^{x+x^2 \log (3 x)} (72-32 x)-72 x+16 x^2} \, dx \]
Mathematica 12.3 output
\[ -\frac {4 x}{9-4 x+4\ 3^{x^2} e^x x^{x^2}} \]