\[ \int \frac {e^{20 x+x \log \left (\frac {1-x \log \left (\frac {e^{-x} \log (2)}{x}\right )}{x}\right )} \left (-19-x-x^2+20 x \log \left (\frac {e^{-x} \log (2)}{x}\right )+\left (-1+x \log \left (\frac {e^{-x} \log (2)}{x}\right )\right ) \log \left (\frac {1-x \log \left (\frac {e^{-x} \log (2)}{x}\right )}{x}\right )\right )}{-1+x \log \left (\frac {e^{-x} \log (2)}{x}\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{x \left (20+\ln \left (\frac {1}{x}-\ln \left (\frac {\ln \left (2\right ) {\mathrm e}^{-x}}{x}\right )\right )\right )} \]
command
integrate(((x*log(log(2)/exp(x)/x)-1)*log((-x*log(log(2)/exp(x)/x)+1)/x)+20*x*log(log(2)/exp(x)/x)-x^2-x-19)*exp(x*log((-x*log(log(2)/exp(x)/x)+1)/x)+20*x)/(x*log(log(2)/exp(x)/x)-1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ e^{\left (x \log \left (\frac {1}{x} - \log \left (\frac {e^{\left (-x\right )} \log \left (2\right )}{x}\right )\right ) + 20 \, x\right )} \]