\[ \int \frac {-120-120 e^2+e^{e^{3 x^2}} \left (-24-24 e^2-288 e^{3 x^2} x\right )}{125 e^{x+e^2 x}+75 e^{e^{3 x^2}+x+e^2 x}+15 e^{2 e^{3 x^2}+x+e^2 x}+e^{3 e^{3 x^2}+x+e^2 x}} \, dx \]
Optimal antiderivative \[ \frac {6 \,{\mathrm e}^{-x -{\mathrm e}^{2} x}}{\left (5+{\mathrm e}^{{\mathrm e}^{3 x^{2}}}\right ) \left (\frac {5}{4}+\frac {{\mathrm e}^{{\mathrm e}^{3 x^{2}}}}{4}\right )} \]
command
Int[(-120 - 120*E^2 + E^E^(3*x^2)*(-24 - 24*E^2 - 288*E^(3*x^2)*x))/(125*E^(x + E^2*x) + 75*E^(E^(3*x^2) + x + E^2*x) + 15*E^(2*E^(3*x^2) + x + E^2*x) + E^(3*E^(3*x^2) + x + E^2*x)),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-120-120 e^2+e^{e^{3 x^2}} \left (-24-24 e^2-288 e^{3 x^2} x\right )}{125 e^{x+e^2 x}+75 e^{e^{3 x^2}+x+e^2 x}+15 e^{2 e^{3 x^2}+x+e^2 x}+e^{3 e^{3 x^2}+x+e^2 x}} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {24 e^{-\left (\left (1+e^2\right ) x\right )}}{\left (e^{e^{3 x^2}}+5\right )^2} \]