\[ \int \frac {\left (-3 e^6+e^3 (-5-2 x)\right ) \log (4)+\left (-3 e^6+e^3 (-5-2 x)\right ) \log (\log (4 \log (2)))}{25 x^2+9 e^6 x^2+10 x^3+x^4+e^3 \left (30 x^2+6 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {\ln \left (\ln \left (4 \ln \left (2\right )\right )\right )+2 \ln \left (2\right )}{x \left (\left (5+x \right ) {\mathrm e}^{-3}+3\right )} \]
command
integrate(((-3*exp(3)^2+(-2*x-5)*exp(3))*log(log(4*log(2)))+2*(-3*exp(3)^2+(-2*x-5)*exp(3))*log(2))/(9*x^2*exp(3)^2+(6*x^3+30*x^2)*exp(3)+x^4+10*x^3+25*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {4 \, e^{6} \log \left (2\right )^{2} + 4 \, e^{6} \log \left (2\right ) \log \left (\log \left (4 \, \log \left (2\right )\right )\right ) + e^{6} \log \left (\log \left (4 \, \log \left (2\right )\right )\right )^{2}}{2 \, {\left (3 \, x e^{6} + {\left (x^{2} + 5 \, x\right )} e^{3}\right )} \log \left (2\right ) + {\left (3 \, x e^{6} + {\left (x^{2} + 5 \, x\right )} e^{3}\right )} \log \left (\log \left (4 \, \log \left (2\right )\right )\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________