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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