\[ \int \frac {e^{\frac {x^2}{6+14 x+6 x^2+4 x^3}} \left (6 x+7 x^2-2 x^4\right )}{18+84 x+134 x^2+108 x^3+74 x^4+24 x^5+8 x^6} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {x}{2 \left (\frac {3+x}{x}+x \right ) \left (1+2 x \right )}} \]
command
Int[(E^(x^2/(6 + 14*x + 6*x^2 + 4*x^3))*(6*x + 7*x^2 - 2*x^4))/(18 + 84*x + 134*x^2 + 108*x^3 + 74*x^4 + 24*x^5 + 8*x^6),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{\frac {x^2}{6+14 x+6 x^2+4 x^3}} \left (6 x+7 x^2-2 x^4\right )}{18+84 x+134 x^2+108 x^3+74 x^4+24 x^5+8 x^6} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{\frac {x^2}{2 \left (2 x^3+3 x^2+7 x+3\right )}} \]