$\displaystyle \int \dfrac{\ln(\ln x)}{x\ln x}dx$ hint?
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Let u= ln(x) seems a pretty obvious first step!
put ln(lnx)=t,
$\displaystyle \int \dfrac{\ln(\ln x)}{x\ln x}dx$ $\displaystyle u = \ln x$ $\displaystyle du = \dfrac{1}{x} dx$ $\displaystyle \int \dfrac{\ln(u)}{du}$ ??? Correct? Next step?
$\displaystyle \int \frac{\ln u}{u}du = \frac{1}{2}(\ln u)^{2}+c=\frac{1}{2}(\ln (\ln x))^{2}+c$ With the last expression obtained by back substituting $\displaystyle u=\ln x$
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