\[ \int \frac {25-20 x+5 e x+4 x^2+e^8 x^4+e^4 \left (10 x^2-4 x^3-e x^3\right )}{e^9 x^5+e \left (25 x-20 x^2+4 x^3\right )+e^5 \left (10 x^3-4 x^4\right )} \, dx \]
Optimal antiderivative \[ 5+\ln \left (x \right ) {\mathrm e}^{-1}+\frac {x}{-2 x +x^{2} {\mathrm e}^{4}+5} \]
command
integrate((x^4*exp(2)^4+(-x^3*exp(1)-4*x^3+10*x^2)*exp(2)^2+5*x*exp(1)+4*x^2-20*x+25)/(x^5*exp(1)*exp(2)^4+(-4*x^4+10*x^3)*exp(1)*exp(2)^2+(4*x^3-20*x^2+25*x)*exp(1)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ e^{\left (-1\right )} \log \left ({\left | x \right |}\right ) + \frac {x}{x^{2} e^{4} - 2 \, x + 5} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________