\[ \int \frac {-5-22 x-4 x^2+2 e^{-2-x} (16+3 x)}{-5 x-x^2+2 e^{-2-x} (5+x)} \, dx \]
Optimal antiderivative \[ \ln \left ({\mathrm e}^{2 x} \left (5+x \right ) \left ({\mathrm e}^{\ln \left (2\right )-x -2}-x \right )\right )+2 x +1 \]
command
Int[(-5 - 22*x - 4*x^2 + 2*E^(-2 - x)*(16 + 3*x))/(-5*x - x^2 + 2*E^(-2 - x)*(5 + x)),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ 3 x+\log (x+5)+\log \left (2-e^{x+2} x\right ) \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {-5-22 x-4 x^2+2 e^{-2-x} (16+3 x)}{-5 x-x^2+2 e^{-2-x} (5+x)} \, dx \]________________________________________________________________________________________