\[ \int \frac {-2592 x^2+144 x^3+576 x^5+e^4 \left (-18+4 x^3\right )+e^2 \left (432 x-96 x^4\right )}{3 e^4 x^3-72 e^2 x^4+432 x^5} \, dx \]
Optimal antiderivative \[ \frac {4 x}{3}+\frac {4}{-12 x +{\mathrm e}^{2}}+\frac {3}{x^{2}} \]
command
integrate(((4*x^3-18)*exp(2)^2+(-96*x^4+432*x)*exp(2)+576*x^5+144*x^3-2592*x^2)/(3*x^3*exp(2)^2-72*x^4*exp(2)+432*x^5),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {4}{3} \, x - \frac {4}{12 \, x - e^{2}} + \frac {3}{x^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________