TITLE: Evaluating $\int \frac{\operatorname dx}{x\log x}$
QUESTION [8 upvotes]: How to integrate $\frac{1}{x\log x}$?
Could you give me some ideas on how to integrate this? thanks.
i've tried setting $u=(\log x)^{-1}$. 
$\dfrac{\mathrm du}{\mathrm dx} = x^{-1}$
But it didnt work...

REPLY [4 votes]: Let : 
$$u = \log{x}$$
Then,
$$\frac{du}{dx} = \frac{1}{x}$$
$$du = \frac{1}{x}dx$$
Hence,
$$\begin{align}\int\frac{1}{x\log{x}}dx &=\int\frac{1}{\log{x}}\frac{1}{x}dx\\&= \int\frac{1}{u}du \\&= \log{|u|} + C \\&=\log|\log{u}| + C\end{align}$$