\[ \int \frac {-10 e^8-e^4 x^2+x^6 \left (-250-100 x-10 x^2\right )+x^3 \left (-75 x-30 x^2-3 x^3+e^4 (100+20 x)\right )}{5 e^{12} x^2+e^8 x^3 \left (-50 x^2-10 x^3\right )+e^4 x^6 \left (125 x^2+50 x^3+5 x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {\left (2+\frac {x}{5}-\frac {x}{5 \left (\frac {{\mathrm e}^{4}}{5+x}-x^{3}\right )}\right ) {\mathrm e}^{-4}}{x} \]
command
integrate(((-10*x^2-100*x-250)*x^6+((20*x+100)*exp(4)-3*x^3-30*x^2-75*x)*x^3-10*exp(4)^2-x^2*exp(4))/((5*x^4+50*x^3+125*x^2)*exp(4)*x^6+(-10*x^3-50*x^2)*exp(4)^2*x^3+5*x^2*exp(4)^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {{\left (10 \, x^{4} + 50 \, x^{3} + x^{2} + 5 \, x - 10 \, e^{4}\right )} e^{\left (-4\right )}}{5 \, {\left (x^{5} + 5 \, x^{4} - x e^{4}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________