\[ \int \frac {e^4+16 x^4+e^2 \left (8 x+8 x^2\right )}{3 e^4+24 e^2 x^2+48 x^4} \, dx \]
Optimal antiderivative \[ \frac {x}{3}+\frac {x}{3 x +\frac {3 \,{\mathrm e}^{2}}{4 x}}-7 \]
command
integrate((exp(2)^2+(8*x^2+8*x)*exp(2)+16*x^4)/(3*exp(2)^2+24*x^2*exp(2)+48*x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{3} \, x - \frac {e^{2}}{3 \, {\left (4 \, x^{2} + e^{2}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________