\[ \int \frac {-3600+480 x+164 x^2+e^4 \left (3600+3120 x+76 x^2-284 x^3+4 x^4\right )+e^8 \left (180 x^2+180 x^3+45 x^4\right )}{900 x^2-120 x^3+4 x^4+e^4 \left (-1800 x^2-660 x^3+112 x^4-4 x^5\right )+e^8 \left (900 x^2+780 x^3+109 x^4-26 x^5+x^6\right )} \, dx \]
Optimal antiderivative \[ \frac {4}{\left (\frac {2}{2+x}-{\mathrm e}^{4}\right ) x}+\frac {x}{5-\frac {x}{3}}+\frac {2}{15} \]
command
integrate(((45*x^4+180*x^3+180*x^2)*exp(4)^2+(4*x^4-284*x^3+76*x^2+3120*x+3600)*exp(4)+164*x^2+480*x-3600)/((x^6-26*x^5+109*x^4+780*x^3+900*x^2)*exp(4)^2+(-4*x^5+112*x^4-660*x^3-1800*x^2)*exp(4)+4*x^4-120*x^3+900*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {45 \, x^{2} e^{4} + 4 \, x^{2} + 90 \, x e^{4} - 142 \, x - 120}{x^{3} e^{4} - 13 \, x^{2} e^{4} - 2 \, x^{2} - 30 \, x e^{4} + 30 \, x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________