\[ \int \frac {\left (-2 x^2+e^2 (12+8 x)+\left (-10 x^2+e^2 (60+40 x)\right ) \log (5)\right ) \log (\log (25))}{\left (4 e^4-4 e^2 x+x^2\right ) \log (5)} \, dx \]
Optimal antiderivative \[ \frac {\ln \left (2 \ln \left (5\right )\right ) \left (5+\frac {1}{\ln \left (5\right )}\right ) x \left (3+x \right )}{{\mathrm e}^{2}-\frac {x}{2}} \]
command
integrate((((40*x+60)*exp(2)-10*x^2)*log(5)+(8*x+12)*exp(2)-2*x^2)*log(2*log(5))/(4*exp(2)^2-4*exp(2)*x+x^2)/log(5),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {2 \, {\left (5 \, x \log \left (5\right ) + x + \frac {2 \, {\left (10 \, e^{4} \log \left (5\right ) + 15 \, e^{2} \log \left (5\right ) + 2 \, e^{4} + 3 \, e^{2}\right )}}{x - 2 \, e^{2}}\right )} \log \left (2 \, \log \left (5\right )\right )}{\log \left (5\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________