Evaluating $\int\frac{\mathrm{d}u}{u\log u}$. I know we use $u$-substitution for $\log u$ and then we find the derivative but after that i'm confused. This is because the question is already using $u$ as a variable. Any explanation would be appreciated.
$$\int\frac{\mathrm{d}u}{u\log u}$$

If $x=\log u$, then $dx/du=1/u$, so we have
$$\int\frac{du}{u\log u}=\int\frac{dx}{x}=\log|x|+C=\log|\log u|+C$$
