\[ \int \frac {-2 e x^2+e^{\frac {1}{2} \left (28+e^4\right )} \left (-2 e^5+4 e x\right )}{e^8 x^2-2 e^4 x^3+x^4} \, dx \]
Optimal antiderivative \[ \frac {2 \left ({\mathrm e}^{\frac {{\mathrm e}^{4}}{2}+14}-x \right ) {\mathrm e}}{x \left ({\mathrm e}^{4}-x \right )} \]
command
integrate(((-2*exp(1)*exp(4)+4*x*exp(1))*exp(1/2*exp(4)+14)-2*x^2*exp(1))/(x^2*exp(4)^2-2*x^3*exp(4)+x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 \, {\left (x e - e^{\left (\frac {1}{2} \, e^{4} + 15\right )}\right )}}{x^{2} - x e^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________