\[ \int \frac {-1576 x^4+36 x^6+e^8 \left (-300 x^2-80 x^3-4 x^4\right )+e^4 \left (1600 x^3+280 x^4\right )}{620944 x^4+370360 x^5+83593 x^6+8460 x^7+324 x^8+e^{16} \left (2500+2000 x+600 x^2+80 x^3+4 x^4\right )+e^{12} \left (-40000 x-30000 x^2-8400 x^3-1040 x^4-48 x^5\right )+e^8 \left (238800 x^2+167020 x^3+43552 x^4+5020 x^5+216 x^6\right )+e^4 \left (-630400 x^3-408640 x^4-99112 x^5-10680 x^6-432 x^7\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{6+\frac {5 x}{2}-\left (\frac {\left (4 x -{\mathrm e}^{4}\right ) \left (5+x \right )}{x}-x \right )^{2}} \]
command
integrate(((-4*x^4-80*x^3-300*x^2)*exp(4)^2+(280*x^4+1600*x^3)*exp(4)+36*x^6-1576*x^4)/((4*x^4+80*x^3+600*x^2+2000*x+2500)*exp(4)^4+(-48*x^5-1040*x^4-8400*x^3-30000*x^2-40000*x)*exp(4)^3+(216*x^6+5020*x^5+43552*x^4+167020*x^3+238800*x^2)*exp(4)^2+(-432*x^7-10680*x^6-99112*x^5-408640*x^4-630400*x^3)*exp(4)+324*x^8+8460*x^7+83593*x^6+370360*x^5+620944*x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {2 \, x^{3}}{18 \, x^{4} - 12 \, x^{3} e^{4} + 235 \, x^{3} + 2 \, x^{2} e^{8} - 140 \, x^{2} e^{4} + 788 \, x^{2} + 20 \, x e^{8} - 400 \, x e^{4} + 50 \, e^{8}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________