\[ \int \frac {e^{5/2} \left (50 x-25 x^2\right )}{16 x^4+e^5 \left (10000-20000 x+10000 x^2\right )+e^{5/2} \left (-800 x^2+800 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{-16 x +\frac {400 \left (1-x \right ) {\mathrm e}^{\frac {5}{2}}}{x}} \]
command
integrate((-25*x^2+50*x)*exp(5/2)/((10000*x^2-20000*x+10000)*exp(5/2)^2+(800*x^3-800*x^2)*exp(5/2)+16*x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {25 \, {\left (x - 1\right )} e^{\frac {5}{2}}}{16 \, {\left (x^{2} + 25 \, x e^{\frac {5}{2}} - 25 \, e^{\frac {5}{2}}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {undef} \]________________________________________________________________________________________