\[ \int \frac {-50 e^4-2 x^2+8 x^3+e^2 \left (-20 x+60 x^2\right )}{75 e^4+30 e^2 x+3 x^2} \, dx \]
Optimal antiderivative \[ -\frac {2 x}{3}+3+\frac {4 x^{3}}{3 \left (5 \,{\mathrm e}^{2}+x \right )} \]
command
integrate((-50*exp(2)^2+(60*x^2-20*x)*exp(2)+8*x^3-2*x^2)/(75*exp(2)^2+30*exp(2)*x+3*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {4}{3} \, x^{2} - \frac {20}{3} \, x e^{2} - \frac {2}{3} \, x - \frac {500 \, e^{6}}{3 \, {\left (x + 5 \, e^{2}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________