\[ \int \frac {40-100 x^2-4 e^{32} x^4+e^{16} \left (-16 x+40 x^3\right )}{25 x^2-10 e^{16} x^3+e^{32} x^4} \, dx \]
Optimal antiderivative \[ \frac {8}{x^{2} \left ({\mathrm e}^{16}-\frac {5}{x}\right )}-4 x \]
command
integrate((-4*x^4*exp(16)^2+(40*x^3-16*x)*exp(16)-100*x^2+40)/(x^4*exp(16)^2-10*x^3*exp(16)+25*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -4 \, x + \frac {8}{x^{2} e^{16} - 5 \, x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________