\[ \int \frac {8 e^4 x+e^5 \left (4-16 x^3\right )}{-x^{10}+e \left (-5 x^9+5 x^{12}\right )+e^2 \left (-10 x^8+20 x^{11}-10 x^{14}\right )+e^3 \left (-10 x^7+30 x^{10}-30 x^{13}+10 x^{16}\right )+e^4 \left (-5 x^6+20 x^9-30 x^{12}+20 x^{15}-5 x^{18}\right )+e^5 \left (-x^5+5 x^8-10 x^{11}+10 x^{14}-5 x^{17}+x^{20}\right )} \, dx \]
Optimal antiderivative \[ \frac {1}{\left (x^{2} \left ({\mathrm e}^{-1}-x^{2}\right )+x \right )^{4}} \]
command
integrate(((-16*x^3+4)*exp(1)^5+8*x*exp(1)^4)/((x^20-5*x^17+10*x^14-10*x^11+5*x^8-x^5)*exp(1)^5+(-5*x^18+20*x^15-30*x^12+20*x^9-5*x^6)*exp(1)^4+(10*x^16-30*x^13+30*x^10-10*x^7)*exp(1)^3+(-10*x^14+20*x^11-10*x^8)*exp(1)^2+(5*x^12-5*x^9)*exp(1)-x^10),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {e^{20}}{{\left (x^{2} e^{4} - {\left (x^{4} - x\right )} e^{5}\right )}^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________