Question

Solve:
$\int \frac{1}{x\log x}dx$

Answer 1

We have,

$\int \frac{1}{x\log x}dx$

put,

$\begin{array}{c}z=\log x\\ dx=\frac{1}{x}dx\end{array}$

$\begin{array}{c}\int \frac{dz}{z}\\ =\log z+C\\ =\log \left(\log x\right)+C\end{array}$