\[ \int \frac {e^{20} \left (548371200000000 x^3+172947840000000 x^4+23828513280000 x^5+1873311897600 x^6+91912863744 x^7+2882018304 x^8+56398848 x^9+629760 x^{10}+3072 x^{11}\right )}{152587890625 x^8+48828125000 x^9+6835937500 x^{10}+546875000 x^{11}+27343750 x^{12}+875000 x^{13}+17500 x^{14}+200 x^{15}+x^{16}+e^{40} \left (218971048064843776+67375707096875008 x+9069806724579328 x^2+697677440352256 x^3+33542184632320 x^4+1032067219456 x^5+19847446528 x^6+218103808 x^7+1048576 x^8\right )+e^{20} \left (365580800000000 x^4+114736128000000 x^5+15753287680000 x^6+1235891404800 x^7+60596226048 x^8+1901371392 x^9+37285888 x^{10}+417792 x^{11}+2048 x^{12}\right )} \, dx \]
Optimal antiderivative \[ \frac {3}{\frac {256 \,{\mathrm e}^{20} \left (6+\frac {6}{x +25}\right )^{4}}{81 x^{4}}+4} \]
command
integrate((3072*x^11+629760*x^10+56398848*x^9+2882018304*x^8+91912863744*x^7+1873311897600*x^6+23828513280000*x^5+172947840000000*x^4+548371200000000*x^3)*exp(5)^4/((1048576*x^8+218103808*x^7+19847446528*x^6+1032067219456*x^5+33542184632320*x^4+697677440352256*x^3+9069806724579328*x^2+67375707096875008*x+218971048064843776)*exp(5)^8+(2048*x^12+417792*x^11+37285888*x^10+1901371392*x^9+60596226048*x^8+1235891404800*x^7+15753287680000*x^6+114736128000000*x^5+365580800000000*x^4)*exp(5)^4+x^16+200*x^15+17500*x^14+875000*x^13+27343750*x^12+546875000*x^11+6835937500*x^10+48828125000*x^9+152587890625*x^8),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {768 \, {\left (x^{4} + 104 \, x^{3} + 4056 \, x^{2} + 70304 \, x + 456976\right )} e^{20}}{x^{8} + 100 \, x^{7} + 3750 \, x^{6} + 62500 \, x^{5} + 1024 \, x^{4} e^{20} + 390625 \, x^{4} + 106496 \, x^{3} e^{20} + 4153344 \, x^{2} e^{20} + 71991296 \, x e^{20} + 467943424 \, e^{20}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________