Try to compute $\int\frac{dx}{x\ln x}$ I compute it this way: first we have $x>0$. \begin{align*} \int\frac{dx}{x\ln x} &=\int\frac{d(\ln x)}{\ln x}\\ &=\ln|\ln x|+C \end{align*} But the answer to the problem is $\ln\ln x+C$. Which one is right? Thanks!
Source Григорий Михайлович Фихтенгольц