\[ \int \frac {4 (5+i \pi )^2-2 e^8 x^2+4 e^{16} x^4+(5+i \pi ) \left (-2-8 e^8 x^2\right )}{(5+i \pi )^2-2 e^8 (5+i \pi ) x^2+e^{16} x^4} \, dx \]
Optimal antiderivative \[ \left (4-\frac {2}{\ln \left (-{\mathrm e}^{5}\right )-x^{2} {\mathrm e}^{8}}\right ) x \]
command
integrate((4*log(-exp(5))^2+(-8*x^2*exp(4)^2-2)*log(-exp(5))+4*x^4*exp(4)^4-2*x^2*exp(4)^2)/(log(-exp(5))^2-2*x^2*exp(4)^2*log(-exp(5))+x^4*exp(4)^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 4 \, x + \frac {2 \, x}{x^{2} e^{8} - \log \left (-e^{5}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________