\[ \int \frac {-30 e^3 x+e^6 x^4+\left (-15+2 e^3 x^3\right ) \log (\log (2))+x^2 \log ^2(\log (2))}{e^6 x^4+2 e^3 x^3 \log (\log (2))+x^2 \log ^2(\log (2))} \, dx \]
Optimal antiderivative \[ x -\frac {15 \left (2 x -\frac {1}{x \,{\mathrm e}^{3}+\ln \left (\ln \left (2\right )\right )}\right )}{x} \]
command
integrate((x^2*log(log(2))^2+(2*x^3*exp(3)-15)*log(log(2))+x^4*exp(3)^2-30*x*exp(3))/(x^2*log(log(2))^2+2*x^3*exp(3)*log(log(2))+x^4*exp(3)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x + \frac {15}{x^{2} e^{3} + x \log \left (\log \left (2\right )\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________