\[ \int \frac {e^8 (8+16 x) \log (5)}{16+e^{16}+128 x+384 x^2+512 x^3+256 x^4+e^8 \left (8+32 x+32 x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {\ln \left (5\right )}{\ln \left ({\mathrm e}^{\frac {2 \,{\mathrm e}^{8}}{\left (4 x +2\right )^{2}}}\right )+2} \]
command
integrate((16*x+8)*exp(4)^2*log(5)/(exp(4)^4+(32*x^2+32*x+8)*exp(4)^2+256*x^4+512*x^3+384*x^2+128*x+16),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {e^{8} \log \left (5\right )}{2 \, {\left (16 \, x^{2} + 16 \, x + e^{8} + 4\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________