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Evaluate the following integrals:

Question:

Evaluate the following integrals:

$\int \frac{1}{x \log x \log (\log x)} d x$

Solution:

Assume $\log (\log x)=t$

$d(\log (\log x))=d t$

(use chain rule to differentiate first)

$\Rightarrow \frac{1}{\text { xlogx }} \mathrm{dx}=\mathrm{dt}$

Put $\mathrm{t}$ and $\mathrm{dt}$ in given equation we get

$\Rightarrow \int \frac{\mathrm{dt}}{\mathrm{t}}$

$=\ln |\mathrm{t}|+\mathrm{c}$

But $t=\log (\log (x))$

$=\ln |\log (\log (x))|+c$

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