\[ \int \frac {e^x \left (18-18 x+27 x^2-3 x^3+e^5 \left (-75 x+15 x^2\right )\right )}{-7776 x^2-6480 x^4-2160 x^6+3125 e^{25} x^7-360 x^8-30 x^{10}-x^{12}+e^{20} \left (-18750 x^6-3125 x^8\right )+e^{15} \left (45000 x^5+15000 x^7+1250 x^9\right )+e^{10} \left (-54000 x^4-27000 x^6-4500 x^8-250 x^{10}\right )+e^5 \left (32400 x^3+21600 x^5+5400 x^7+600 x^9+25 x^{11}\right )} \, dx \]
Optimal antiderivative \[ \frac {3 \,{\mathrm e}^{x}}{x \left (x^{2}-5 x \,{\mathrm e}^{5}+6\right )^{4}} \]
command
integrate(((15*x^2-75*x)*exp(5)-3*x^3+27*x^2-18*x+18)*exp(x)/(3125*x^7*exp(5)^5+(-3125*x^8-18750*x^6)*exp(5)^4+(1250*x^9+15000*x^7+45000*x^5)*exp(5)^3+(-250*x^10-4500*x^8-27000*x^6-54000*x^4)*exp(5)^2+(25*x^11+600*x^9+5400*x^7+21600*x^5+32400*x^3)*exp(5)-x^12-30*x^10-360*x^8-2160*x^6-6480*x^4-7776*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {x^{8} e^{x} - 20 \, x^{7} e^{\left (x + 5\right )} + 150 \, x^{6} e^{\left (x + 10\right )} + 24 \, x^{6} e^{x} - 500 \, x^{5} e^{\left (x + 15\right )} - 360 \, x^{5} e^{\left (x + 5\right )} + 625 \, x^{4} e^{\left (x + 20\right )} + 1800 \, x^{4} e^{\left (x + 10\right )} + 216 \, x^{4} e^{x} - 3000 \, x^{3} e^{\left (x + 15\right )} - 2160 \, x^{3} e^{\left (x + 5\right )} + 5400 \, x^{2} e^{\left (x + 10\right )} + 864 \, x^{2} e^{x} - 4320 \, x e^{\left (x + 5\right )} - 1296 \, e^{x}}{432 \, {\left (x^{9} - 20 \, x^{8} e^{5} + 150 \, x^{7} e^{10} + 24 \, x^{7} - 500 \, x^{6} e^{15} - 360 \, x^{6} e^{5} + 625 \, x^{5} e^{20} + 1800 \, x^{5} e^{10} + 216 \, x^{5} - 3000 \, x^{4} e^{15} - 2160 \, x^{4} e^{5} + 5400 \, x^{3} e^{10} + 864 \, x^{3} - 4320 \, x^{2} e^{5} + 1296 \, x\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________