43.36 Problem number 5600

$$\int \frac{e^{20x+x\log \left(\frac{1-x\log \left(\frac{e^{-x}\log (2)}{x}\right)}{x}\right)}(-19-x-x^2+20x\log \left(\frac{e^{-x}\log (2)}{x}\right)+(-1+x\log \left(\frac{e^{-x}\log (2)}{x}\right))\log \left(\frac{1-x\log \left(\frac{e^{-x}\log (2)}{x}\right)}{x}\right))}{-1+x\log \left(\frac{e^{-x}\log (2)}{x}\right)}dx$$

Optimal antiderivative $${\mathrm{e}}^{x(20+\ln (\frac{1}{x}-\ln \left(\frac{\ln \left(2\right){\mathrm{e}}^{-x}}{x}\right)))}$$

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

$$e^{(x\log (\frac{1}{x}-\log \left(\frac{e^{(-x)}\log \left(2\right)}{x}\right))+20x)}$$