\[ \int \frac {4 x+2 e^{40} x^2+2 x^4+e^{20} \left (-2-4 x^3\right )}{e^{40} x^2-2 e^{20} x^3+x^4} \, dx \]
Optimal antiderivative \[ 2 x +\frac {2}{x \left ({\mathrm e}^{20}-x \right )}-\frac {{\mathrm e}^{\frac {4}{3}}}{3} \]
command
integrate((2*x^2*exp(5)^8+(-4*x^3-2)*exp(5)^4+2*x^4+4*x)/(x^2*exp(5)^8-2*x^3*exp(5)^4+x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 2 \, x - \frac {2}{x^{2} - x e^{20}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________