\[ \int \frac {40 e^5+550 x-200 x^2}{-33275 x^4+18150 x^5-3300 x^6+200 x^7+e^{10} \left (-5324+2904 x-528 x^2+32 x^3\right )+e^5 \left (26620 x^2-14520 x^3+2640 x^4-160 x^5\right )} \, dx \]
Optimal antiderivative \[ \frac {1}{\left (x^{2}-\frac {2 \,{\mathrm e}^{5}}{5}\right ) \left (-2 x +11\right )^{2}} \]
command
integrate((40*exp(5)-200*x^2+550*x)/((32*x^3-528*x^2+2904*x-5324)*exp(5)^2+(-160*x^5+2640*x^4-14520*x^3+26620*x^2)*exp(5)+200*x^7-3300*x^6+18150*x^5-33275*x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {25 \, {\left (220 \, x + 8 \, e^{5} + 605\right )}}{{\left (5 \, x^{2} - 2 \, e^{5}\right )} {\left (64 \, e^{10} - 9680 \, e^{5} + 366025\right )}} - \frac {20 \, {\left (220 \, x + 8 \, e^{5} - 1815\right )}}{{\left (2 \, x - 11\right )}^{2} {\left (64 \, e^{10} - 9680 \, e^{5} + 366025\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________