Question:
Evaluate $\int \frac{\log (\log x)}{x} d x$
Solution:
Let, $\log x=t$
Differentiating both side with respect to $t$
$\frac{1}{x} \frac{d x}{d t}=1 \Rightarrow \frac{d x}{x}=d t$
Note:- Always use direct formula for $\int \log x d x$
$y=\int \log t d t$
$y=t \log t-t+c$
Again, put $t=\log x$
$y=(\log x) \log (\log x)-\log x+c$
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