\[ \int \frac {-2 x^2-12 x^5+e^{10} \left (-2-12 x^3\right )+e^5 \left (-4 x-18 x^2-24 x^4\right )}{e^{10} x^2+2 e^5 x^3+x^4} \, dx \]
Optimal antiderivative \[ \frac {2 x +2-6 \left (x +\frac {3}{{\mathrm e}^{5}+x}\right ) x^{2}}{x} \]
command
integrate(((-12*x^3-2)*exp(5)^2+(-24*x^4-18*x^2-4*x)*exp(5)-12*x^5-2*x^2)/(x^2*exp(5)^2+2*x^3*exp(5)+x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -6 \, x^{2} + \frac {2 \, {\left (9 \, x e^{5} + x + e^{5}\right )}}{x^{2} + x e^{5}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________