\[ \int \frac {8 e^2-768 x+288 x^2}{2304 x^4-1152 x^5+144 x^6+e^4 \left (16-8 x+x^2\right )+e^2 \left (384 x^2-192 x^3+24 x^4\right )} \, dx \]
Optimal antiderivative \[ 1-\frac {1}{\left (x^{2}+\frac {x \left (x +\frac {{\mathrm e}^{2}}{4 x}\right )}{2}\right ) \left (-4+x \right )} \]
command
integrate((8*exp(2)+288*x^2-768*x)/((x^2-8*x+16)*exp(2)^2+(24*x^4-192*x^3+384*x^2)*exp(2)+144*x^6-1152*x^5+2304*x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {8}{12 \, x^{3} - 48 \, x^{2} + x e^{2} - 4 \, e^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________