\[ \int \frac {-4+e^{24} \left (256-4 x^2\right )+e^{48} \left (-4096-6 x+128 x^2-x^4\right )}{4+e^{24} \left (-256+4 x^2\right )+e^{48} \left (4096-128 x^2+x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {3}{x^{2}-64+2 \,{\mathrm e}^{-24}}-\frac {2}{5}-x \]
command
integrate(((-x^4+128*x^2-6*x-4096)*exp(24)^2+(-4*x^2+256)*exp(24)-4)/((x^4-128*x^2+4096)*exp(24)^2+(4*x^2-256)*exp(24)+4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -x + \frac {3 \, e^{24}}{x^{2} e^{24} - 64 \, e^{24} + 2} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________