Answer
$\dfrac{[\ln (\ln x)]^2}{2} +c$
Work Step by Step
Solve $\int\dfrac{\ln (\ln x)}{x \ln x}dx$
Let us $p= \ln (\ln x)$ and $dp=\dfrac{1}{x \ln x}dx$
This implies $\int\dfrac{\ln (\ln x)}{x \ln x}dx= \int p dp$
$= \dfrac{p^2}{2} +c$
$= \dfrac{[\ln (\ln x)]^2}{2} +c$
Hence, $\int\dfrac{\ln (\ln x)}{x \ln x}dx=\dfrac{[\ln (\ln x)]^2}{2} +c$
