\[ \int \frac {20-20 e^2+20 e x-5 x^2}{4 e^2-4 e x+x^2} \, dx \]
Optimal antiderivative \[ \frac {20}{2 \,{\mathrm e}-x}-5 x -4071 \]
command
integrate((-20*exp(1)^2+20*x*exp(1)-5*x^2+20)/(4*exp(1)^2-4*x*exp(1)+x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -5 \, x - \frac {20}{x - 2 \, e} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________