\[ \int \frac {15 e^{5+\frac {x}{3}}+e^5 (6+2 x)}{\left (-6 x+e^{x/3} \left (-15 x+3 x^2\right )\right ) \log \left (\frac {e^{-x/3} \left (2+e^{x/3} (5-x)\right )}{x}\right )} \, dx \]
Optimal antiderivative \[ \ln \! \left (\ln \! \left (\frac {5-x +2 \,{\mathrm e}^{-\frac {x}{3}}}{x}\right )\right ) {\mathrm e}^{5} \]
command
Int[(15*E^(5 + x/3) + E^5*(6 + 2*x))/((-6*x + E^(x/3)*(-15*x + 3*x^2))*Log[(2 + E^(x/3)*(5 - x))/(E^(x/3)*x)]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {15 e^{5+\frac {x}{3}}+e^5 (6+2 x)}{\left (-6 x+e^{x/3} \left (-15 x+3 x^2\right )\right ) \log \left (\frac {e^{-x/3} \left (2+e^{x/3} (5-x)\right )}{x}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^5 \log \left (\log \left (\frac {2 e^{-x/3}}{x}+\frac {5}{x}-1\right )\right ) \]