\[ \int \frac {e^{5+\frac {e^5}{-3-x-x^2+\log (5)}} (1+2 x)}{9+6 x+7 x^2+2 x^3+x^4+\left (-6-2 x-2 x^2\right ) \log (5)+\log ^2(5)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {{\mathrm e}^{5}}{\ln \left (5\right )-x^{2}-x -3}} \]
command
Int[(E^(5 + E^5/(-3 - x - x^2 + Log[5]))*(1 + 2*x))/(9 + 6*x + 7*x^2 + 2*x^3 + x^4 + (-6 - 2*x - 2*x^2)*Log[5] + Log[5]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{5+\frac {e^5}{-3-x-x^2+\log (5)}} (1+2 x)}{9+6 x+7 x^2+2 x^3+x^4+\left (-6-2 x-2 x^2\right ) \log (5)+\log ^2(5)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{-\frac {e^5}{x^2+x+3-\log (5)}} \]