\[ \int \frac {360 x+270 x^2+e^{12} x^2-3 e^8 x^3-x^5+e^4 \left (-120+3 x^4\right )}{-120 x^2-135 x^3+e^{12} x^3-3 e^8 x^4-x^6+e^4 \left (120 x+135 x^2+3 x^5\right )} \, dx \]
Optimal antiderivative \[ \ln \left (x +\frac {\frac {120}{x}+135}{\left ({\mathrm e}^{4}-x \right )^{2}}\right ) \]
command
integrate((x^2*exp(2)^6-3*x^3*exp(2)^4+(3*x^4-120)*exp(2)^2-x^5+270*x^2+360*x)/(x^3*exp(2)^6-3*x^4*exp(2)^4+(3*x^5+135*x^2+120*x)*exp(2)^2-x^6-135*x^3-120*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \log \left (x^{4} - 2 \, x^{3} e^{4} + x^{2} e^{8} + 135 \, x + 120\right ) - 2 \, \log \left ({\left | x - e^{4} \right |}\right ) - \log \left ({\left | x \right |}\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________