Answer
$$\int \frac{dx}{x\ln x}=\ln|\ln x|+C$$
Work Step by Step
$$A=\int \frac{dx}{x\ln x}=\int\Big(\frac{1}{\ln x}\times\frac{dx}{x}\Big)$$
We set $u=\ln x$
Then $$du=\frac{dx}{x}$$
Therefore, $$A=\int\frac{1}{u}du=\ln|u|+C$$ $$A=\ln|\ln x|+C$$