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