\[ \int \frac {-20 x^5+120 x^9-160 x^{11}+60 x^{13}+e^{25} \left (-320+480 x^4-320 x^6+60 x^8\right )+e^{20} \left (-1280 x+480 x^3+1680 x^5-1400 x^7+300 x^9\right )+e^{15} \left (-1600 x^2+960 x^4+2400 x^6-2440 x^8+600 x^{10}\right )+e^{10} \left (-880 x^3+600 x^5+1800 x^7-2120 x^9+600 x^{11}\right )+e^5 \left (-220 x^4+120 x^6+720 x^8-920 x^{10}+300 x^{12}\right )}{e^{25} x^3+5 e^{20} x^4+10 e^{15} x^5+10 e^{10} x^6+5 e^5 x^7+x^8} \, dx \]
Optimal antiderivative \[ 4+\frac {10 \left (\frac {x}{{\mathrm e}^{5}+x}+x^{2}-2\right )^{4}}{x^{2}} \]
command
integrate(((60*x^8-320*x^6+480*x^4-320)*exp(5)^5+(300*x^9-1400*x^7+1680*x^5+480*x^3-1280*x)*exp(5)^4+(600*x^10-2440*x^8+2400*x^6+960*x^4-1600*x^2)*exp(5)^3+(600*x^11-2120*x^9+1800*x^7+600*x^5-880*x^3)*exp(5)^2+(300*x^12-920*x^10+720*x^8+120*x^6-220*x^4)*exp(5)+60*x^13-160*x^11+120*x^9-20*x^5)/(x^3*exp(5)^5+5*x^4*exp(5)^4+10*x^5*exp(5)^3+10*x^6*exp(5)^2+5*x^7*exp(5)+x^8),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 10 \, x^{6} - 40 \, x^{4} - 40 \, x^{3} e^{5} + 40 \, x^{2} e^{10} + 60 \, x^{2} - 40 \, x e^{15} + 120 \, x e^{5} - \frac {160 \, {\left (2 \, x - e^{5}\right )} e^{\left (-5\right )}}{x^{2}} - \frac {10 \, {\left (4 \, x^{3} e^{30} + 12 \, x^{3} e^{10} - 32 \, x^{3} + 12 \, x^{2} e^{35} - 6 \, x^{2} e^{25} + 48 \, x^{2} e^{15} - 113 \, x^{2} e^{5} + 12 \, x e^{40} - 12 \, x e^{30} + 64 \, x e^{20} - 136 \, x e^{10} + 4 \, e^{45} - 6 \, e^{35} + 28 \, e^{25} - 56 \, e^{15}\right )} e^{\left (-5\right )}}{{\left (x + e^{5}\right )}^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________