\[ \int \frac {e^{\frac {100+e^3}{1+2 x+x^2}} \left (-999+e^3 (-10-2 x)-197 x+3 x^2+x^3\right )}{1+3 x+3 x^2+x^3} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {{\mathrm e}^{3}+100}{\left (1+x \right )^{2}}} \left (5+x \right ) \]
command
Int[(E^((100 + E^3)/(1 + 2*x + x^2))*(-999 + E^3*(-10 - 2*x) - 197*x + 3*x^2 + x^3))/(1 + 3*x + 3*x^2 + x^3),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{\frac {100+e^3}{1+2 x+x^2}} \left (-999+e^3 (-10-2 x)-197 x+3 x^2+x^3\right )}{1+3 x+3 x^2+x^3} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{\frac {100+e^3}{(x+1)^2}} (x+1)+4 e^{\frac {100+e^3}{(x+1)^2}} \]