\[ \int \frac {-300+25 e^3-200 x}{144 x^2+e^6 x^2+96 x^3+16 x^4+e^3 \left (-24 x^2-8 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {25}{\left (12+4 x -{\mathrm e}^{3}\right ) x} \]
command
integrate((25*exp(3)-200*x-300)/(x^2*exp(3)^2+(-8*x^3-24*x^2)*exp(3)+16*x^4+96*x^3+144*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {25}{4 \, x^{2} - x e^{3} + 12 \, x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________