\[ \int \frac {16 e^{e^x}-16 e^{e^x} \log (x) \log (\log (x)) \log (\log (\log (x)))-16 e^{e^x+x} x \log (x) \log (\log (x)) \log (\log (\log (x))) \log \left (\frac {\log (\log (\log (x)))}{x}\right )}{x \log (x) \log (\log (x)) \log (\log (\log (x))) \log ^2\left (\frac {\log (\log (\log (x)))}{x}\right )} \, dx \]
Optimal antiderivative \[ -82-\frac {16 \,{\mathrm e}^{{\mathrm e}^{x}}}{\ln \left (\frac {\ln \left (\ln \left (\ln \left (x \right )\right )\right )}{x}\right )} \]
command
integrate((-16*x*exp(x)*ln(x)*exp(exp(x))*ln(ln(x))*ln(ln(ln(x)))*ln(ln(ln(ln(x)))/x)-16*ln(x)*exp(exp(x))*ln(ln(x))*ln(ln(ln(x)))+16*exp(exp(x)))/x/ln(x)/ln(ln(x))/ln(ln(ln(x)))/ln(ln(ln(ln(x)))/x)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \frac {16 e^{e^{x}}}{\log {\left (\frac {\log {\left (\log {\left (\log {\left (x \right )} \right )} \right )}}{x} \right )}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________