\[ \int \frac {-6 e^5-6 x+\left (-6 x-6 x^2-2 x^6+e^5 \left (-6 x-2 x^5\right )\right ) \log \left (\frac {2}{x}\right )+\left (6 e^5 x^4+6 x^5\right ) \log \left (\frac {2}{x}\right ) \log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )+\left (-6 e^5 x^3-6 x^4\right ) \log \left (\frac {2}{x}\right ) \log ^2\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )+\left (2 e^5 x^2+2 x^3\right ) \log \left (\frac {2}{x}\right ) \log ^3\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )}{\left (-e^5 x^4-x^5\right ) \log \left (\frac {2}{x}\right )+\left (3 e^5 x^3+3 x^4\right ) \log \left (\frac {2}{x}\right ) \log \left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )+\left (-3 e^5 x^2-3 x^3\right ) \log \left (\frac {2}{x}\right ) \log ^2\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )+\left (e^5 x+x^2\right ) \log \left (\frac {2}{x}\right ) \log ^3\left (\frac {5 \log \left (\frac {2}{x}\right )}{e^5+x}\right )} \, dx \]
Optimal antiderivative \[ x^{2}-\frac {3}{\left (\ln \left (\frac {5 \ln \left (\frac {2}{x}\right )}{{\mathrm e}^{5}+x}\right )-x \right )^{2}} \]
command
integrate(((2*x^2*exp(5)+2*x^3)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^3+(-6*x^3*exp(5)-6*x^4)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^2+(6*x^4*exp(5)+6*x^5)*log(2/x)*log(5*log(2/x)/(exp(5)+x))+((-2*x^5-6*x)*exp(5)-2*x^6-6*x^2-6*x)*log(2/x)-6*exp(5)-6*x)/((x*exp(5)+x^2)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^3+(-3*x^2*exp(5)-3*x^3)*log(2/x)*log(5*log(2/x)/(exp(5)+x))^2+(3*x^3*exp(5)+3*x^4)*log(2/x)*log(5*log(2/x)/(exp(5)+x))+(-x^4*exp(5)-x^5)*log(2/x)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________