Question

$\int \frac{ln\left(lnx\right)}{xlnx}dx,(x>0)$

Answer 1

$\int \frac{\ln \left(\ln x\right)}{x\ln x}dx$

$\ln \left(\ln x\right)=t$

$\frac{1}{\ln x}\left(\frac{1}{x}\right)=\frac{dt}{dx}\Rightarrow dx=x\ln xdt$

$\int tdt\Rightarrow \frac{t^2}{2}=\frac{\ln (\ln x{)}^2}{2}$