\[ \int \frac {\left (-8 x-2 x \log \left (\frac {1}{x}\right )\right ) \log \left (16+8 \log \left (\frac {1}{x}\right )+\log ^2\left (\frac {1}{x}\right )\right )+\left (8+\left (64+16 \log \left (\frac {1}{x}\right )\right ) \log \left (16+8 \log \left (\frac {1}{x}\right )+\log ^2\left (\frac {1}{x}\right )\right )\right ) \log \left (\frac {\log \left (16+8 \log \left (\frac {1}{x}\right )+\log ^2\left (\frac {1}{x}\right )\right )}{x^4}\right )}{\left (4 x^3+x^3 \log \left (\frac {1}{x}\right )\right ) \log \left (16+8 \log \left (\frac {1}{x}\right )+\log ^2\left (\frac {1}{x}\right )\right )+\left (8 x^2+2 x^2 \log \left (\frac {1}{x}\right )\right ) \log \left (16+8 \log \left (\frac {1}{x}\right )+\log ^2\left (\frac {1}{x}\right )\right ) \log ^2\left (\frac {\log \left (16+8 \log \left (\frac {1}{x}\right )+\log ^2\left (\frac {1}{x}\right )\right )}{x^4}\right )+\left (4 x+x \log \left (\frac {1}{x}\right )\right ) \log \left (16+8 \log \left (\frac {1}{x}\right )+\log ^2\left (\frac {1}{x}\right )\right ) \log ^4\left (\frac {\log \left (16+8 \log \left (\frac {1}{x}\right )+\log ^2\left (\frac {1}{x}\right )\right )}{x^4}\right )} \, dx \]
Optimal antiderivative \[ \frac {2}{x +\ln \left (\frac {\ln \left (\left (4+\ln \left (\frac {1}{x}\right )\right )^{2}\right )}{x^{4}}\right )^{2}} \]
command
integrate((((16*log(1/x)+64)*log(log(1/x)^2+8*log(1/x)+16)+8)*log(log(log(1/x)^2+8*log(1/x)+16)/x^4)+(-2*x*log(1/x)-8*x)*log(log(1/x)^2+8*log(1/x)+16))/((x*log(1/x)+4*x)*log(log(1/x)^2+8*log(1/x)+16)*log(log(log(1/x)^2+8*log(1/x)+16)/x^4)^4+(2*x^2*log(1/x)+8*x^2)*log(log(1/x)^2+8*log(1/x)+16)*log(log(log(1/x)^2+8*log(1/x)+16)/x^4)^2+(x^3*log(1/x)+4*x^3)*log(log(1/x)^2+8*log(1/x)+16)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2}{16 \, \log \left (x\right )^{2} - 8 \, \log \left (x\right ) \log \left (\log \left (\log \left (x\right )^{2} - 8 \, \log \left (x\right ) + 16\right )\right ) + \log \left (\log \left (\log \left (x\right )^{2} - 8 \, \log \left (x\right ) + 16\right )\right )^{2} + x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________