\[ \int \frac {e^4 \left (480 x-144 x^2-120 x^3+12 x^4\right )+e^2 \left (1600 x^2-640 x^3-1200 x^4+160 x^5\right )}{25600 x^2+19200 x^4+4800 x^6+400 x^8+e^4 \left (576+432 x^2+108 x^4+9 x^6\right )+e^2 \left (7680 x+5760 x^3+1440 x^5+120 x^7\right )} \, dx \]
Optimal antiderivative \[ \frac {x^{2} \left (5-x \right )}{\left (\frac {3}{4}+5 x \,{\mathrm e}^{-2}\right ) \left (x^{2}+4\right )^{2}} \]
command
integrate(((12*x^4-120*x^3-144*x^2+480*x)*exp(2)^2+(160*x^5-1200*x^4-640*x^3+1600*x^2)*exp(2))/((9*x^6+108*x^4+432*x^2+576)*exp(2)^2+(120*x^7+1440*x^5+5760*x^3+7680*x)*exp(2)+400*x^8+4800*x^6+19200*x^4+25600*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {720 \, {\left (3 \, e^{8} + 100 \, e^{6}\right )}}{{\left (20 \, x + 3 \, e^{2}\right )} {\left (81 \, e^{8} + 28800 \, e^{4} + 2560000\right )}} - \frac {4 \, {\left (27 \, x^{3} e^{8} + 900 \, x^{3} e^{6} - 135 \, x^{2} e^{8} + 1440 \, x^{2} e^{6} + 128000 \, x^{2} e^{2} - 19200 \, x e^{4} - 640000 \, x e^{2} + 2880 \, e^{6} + 96000 \, e^{4}\right )}}{{\left (x^{2} + 4\right )}^{2} {\left (81 \, e^{8} + 28800 \, e^{4} + 2560000\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________