Evaluate the following integrals:

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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