\[ \int \frac {e^{5 e^{-\frac {-2-3 x+x^2}{-3+x}}} \left (-275+150 x-25 x^2\right )}{e^{5 e^{-\frac {-2-3 x+x^2}{-3+x}}+\frac {-2-3 x+x^2}{-3+x}} \left (9-6 x+x^2\right )+e^{\frac {-2-3 x+x^2}{-3+x}} \left (63-42 x+7 x^2\right )} \, dx \]
Optimal antiderivative \[ 5 \ln \left (-7-{\mathrm e}^{5 \,{\mathrm e}^{-x -\frac {2}{-x +3}}}\right ) \]
command
Int[(E^(5/E^((-2 - 3*x + x^2)/(-3 + x)))*(-275 + 150*x - 25*x^2))/(E^(5/E^((-2 - 3*x + x^2)/(-3 + x)) + (-2 - 3*x + x^2)/(-3 + x))*(9 - 6*x + x^2) + E^((-2 - 3*x + x^2)/(-3 + x))*(63 - 42*x + 7*x^2)),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ 5 \log \left (e^{5 e^{\frac {x^2}{3-x}-\frac {3 x}{3-x}-\frac {2}{3-x}}}+7\right ) \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {e^{5 e^{-\frac {-2-3 x+x^2}{-3+x}}} \left (-275+150 x-25 x^2\right )}{\exp \left (5 e^{-\frac {-2-3 x+x^2}{-3+x}}+\frac {-2-3 x+x^2}{-3+x}\right ) \left (9-6 x+x^2\right )+e^{\frac {-2-3 x+x^2}{-3+x}} \left (63-42 x+7 x^2\right )} \, dx \]________________________________________________________________________________________