\[ \int -\frac {4 \log (2) \log (9)}{x^2+\left (-16 x-32 e^3 x\right ) \log (2)+\left (64+256 e^3+256 e^6\right ) \log ^2(2)} \, dx \]
Optimal antiderivative \[ \frac {2 x \ln \left (3\right )}{\frac {x}{1-\frac {x}{4 \ln \left (2\right )}+4 \,{\mathrm e}^{3}}+x} \]
command
integrate(-8*log(2)*log(3)/((256*exp(3)^2+256*exp(3)+64)*log(2)^2+(-32*x*exp(3)-16*x)*log(2)+x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {8 \, \log \left (3\right ) \log \left (2\right )}{16 \, e^{3} \log \left (2\right ) - x + 8 \, \log \left (2\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________