\[ \int \frac {e^{5 x^2} (2+4 x)+e^{5 x^2} \left (-30 x+10 x^2+10 x^3\right ) \log \left (6561-4374 x-3645 x^2+1458 x^3+729 x^4\right )}{-3+x+x^2} \, dx \]
Optimal antiderivative \[ \ln \! \left (27 \left (x^{2}+x -3\right ) \left (27 x^{2}+27 x -81\right )\right ) {\mathrm e}^{5 x^{2}} \]
command
Int[(E^(5*x^2)*(2 + 4*x) + E^(5*x^2)*(-30*x + 10*x^2 + 10*x^3)*Log[6561 - 4374*x - 3645*x^2 + 1458*x^3 + 729*x^4])/(-3 + x + x^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{5 x^2} (2+4 x)+e^{5 x^2} \left (-30 x+10 x^2+10 x^3\right ) \log \left (6561-4374 x-3645 x^2+1458 x^3+729 x^4\right )}{-3+x+x^2} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{5 x^2} \log \left (729 \left (-x^2-x+3\right )^2\right ) \]