\[ \int \frac {-45-9 e^2 x}{900 x^3+240 e^2 x^4+16 e^4 x^5} \, dx \]
Optimal antiderivative \[ \frac {1}{4 x^{2} \left (10+\frac {4 \,{\mathrm e}^{2} x}{3}\right )} \]
command
integrate((-9*exp(2)*x-45)/(16*x^5*exp(2)^2+240*x^4*exp(2)+900*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {e^{4}}{150 \, {\left (2 \, x e^{2} + 15\right )}} - \frac {2 \, x e^{2} - 15}{600 \, x^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________