\[ \int \frac {9-6 x^2+x^4+e^{-\frac {3 x}{-3+x^2}} \left (9 x+3 x^3\right )}{e^{-\frac {3 x}{-3+x^2}} \left (9 x-6 x^3+x^5\right )+\left (9 x-6 x^3+x^5\right ) \log (x)} \, dx \]
Optimal antiderivative \[ \ln \left (\ln \left (x \right )+{\mathrm e}^{\frac {3 x}{-x^{2}+3}}\right ) \]
command
Int[(9 - 6*x^2 + x^4 + (9*x + 3*x^3)/E^((3*x)/(-3 + x^2)))/((9*x - 6*x^3 + x^5)/E^((3*x)/(-3 + x^2)) + (9*x - 6*x^3 + x^5)*Log[x]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \frac {3 x}{3-x^2}+\log \left (e^{-\frac {3 x}{3-x^2}} \log (x)+1\right ) \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {9-6 x^2+x^4+e^{-\frac {3 x}{-3+x^2}} \left (9 x+3 x^3\right )}{e^{-\frac {3 x}{-3+x^2}} \left (9 x-6 x^3+x^5\right )+\left (9 x-6 x^3+x^5\right ) \log (x)} \, dx \]________________________________________________________________________________________