\[ \int \frac {32 e^8+128 x^4+e^4 \left (24+128 x^2\right )}{9 x^3+16 e^8 x^3+48 x^5+64 x^7+e^4 \left (24 x^3+64 x^5\right )} \, dx \]
Optimal antiderivative \[ -\frac {4}{\frac {3 x}{2 x +\frac {{\mathrm e}^{4}}{x}}+4 x^{2}} \]
command
integrate((32*exp(4)^2+(128*x^2+24)*exp(4)+128*x^4)/(16*x^3*exp(4)^2+(64*x^5+24*x^3)*exp(4)+64*x^7+48*x^5+9*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {4 \, {\left (2 \, x^{2} + e^{4}\right )}}{8 \, x^{4} + 4 \, x^{2} e^{4} + 3 \, x^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________