\[ \int \frac {18 x-10 x^3+e^5 \left (-12-2 x^3\right )}{\left (e^{10} x^3-2 e^5 x^4+x^5\right ) \log \left (\frac {\log ^2(5)}{4}\right )} \, dx \]
Optimal antiderivative \[ \frac {2 x +10-\frac {6}{x^{2}}}{\ln \left (\frac {\ln \left (5\right )^{2}}{4}\right ) \left (-{\mathrm e}^{5}+x \right )} \]
command
integrate(((-2*x^3-12)*exp(5)-10*x^3+18*x)/(x^3*exp(5)^2-2*x^4*exp(5)+x^5)/log(1/4*log(5)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 \, {\left (\frac {{\left (e^{15} + 5 \, e^{10} - 3\right )} e^{\left (-10\right )}}{x - e^{5}} + \frac {3 \, {\left (x + e^{5}\right )} e^{\left (-10\right )}}{x^{2}}\right )}}{\log \left (\frac {1}{4} \, \log \left (5\right )^{2}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________