\[ \int -\frac {1350 e^{\frac {13 x^2+675 \log (3)}{x^2}} \log (3)}{x^3+e^{\frac {13 x^2+675 \log (3)}{x^2}} x^3} \, dx \]
Optimal antiderivative \[ \ln \! \left ({\mathrm e}^{13+\frac {675 \ln \left (3\right )}{x^{2}}}+1\right ) \]
command
Int[(-1350*E^((13*x^2 + 675*Log[3])/x^2)*Log[3])/(x^3 + E^((13*x^2 + 675*Log[3])/x^2)*x^3),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int -\frac {1350 e^{\frac {13 x^2+675 \log (3)}{x^2}} \log (3)}{x^3+e^{\frac {13 x^2+675 \log (3)}{x^2}} x^3} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \log \left (e^{13} 3^{\frac {675}{x^2}}+1\right ) \]