\[ \int \frac {-244140000-e^{12}-585938000 x-644531700 x^2-429687600 x^3-193359382 x^4-61875000 x^5-14437500 x^6-2475000 x^7-309375 x^8-27500 x^9-1650 x^{10}-60 x^{11}-x^{12}+e^8 \left (-1875-1500 x-450 x^2-60 x^3-3 x^4\right )+e^4 \left (-1171874-1875000 x-1312500 x^2-525000 x^3-131250 x^4-21000 x^5-2100 x^6-120 x^7-3 x^8\right )}{488280000 x+2 e^{12} x+1171874000 x^2+1289062200 x^3+859374960 x^4+386718748 x^5+123750000 x^6+28875000 x^7+4950000 x^8+618750 x^9+55000 x^{10}+3300 x^{11}+120 x^{12}+2 x^{13}+e^8 \left (3750 x+3000 x^2+900 x^3+120 x^4+6 x^5\right )+e^4 \left (2343748 x+3750000 x^2+2625000 x^3+1050000 x^4+262500 x^5+42000 x^6+4200 x^7+240 x^8+6 x^9\right )} \, dx \]
Optimal antiderivative \[ \frac {\ln \left (\frac {4}{\frac {x}{\left (\left (5+x \right )^{4}+{\mathrm e}^{4}\right )^{2}}-x}\right )}{2}-3 \]
command
integrate((-exp(4)^3+(-3*x^4-60*x^3-450*x^2-1500*x-1875)*exp(4)^2+(-3*x^8-120*x^7-2100*x^6-21000*x^5-131250*x^4-525000*x^3-1312500*x^2-1875000*x-1171874)*exp(4)-x^12-60*x^11-1650*x^10-27500*x^9-309375*x^8-2475000*x^7-14437500*x^6-61875000*x^5-193359382*x^4-429687600*x^3-644531700*x^2-585938000*x-244140000)/(2*x*exp(4)^3+(6*x^5+120*x^4+900*x^3+3000*x^2+3750*x)*exp(4)^2+(6*x^9+240*x^8+4200*x^7+42000*x^6+262500*x^5+1050000*x^4+2625000*x^3+3750000*x^2+2343748*x)*exp(4)+2*x^13+120*x^12+3300*x^11+55000*x^10+618750*x^9+4950000*x^8+28875000*x^7+123750000*x^6+386718748*x^5+859374960*x^4+1289062200*x^3+1171874000*x^2+488280000*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {1}{2} \, \log \left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + e^{4} + 626\right ) + \log \left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + e^{4} + 625\right ) - \frac {1}{2} \, \log \left (x^{4} + 20 \, x^{3} + 150 \, x^{2} + 500 \, x + e^{4} + 624\right ) - \frac {1}{2} \, \log \left ({\left | x \right |}\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________