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Special Integrals - 1

Evaluate: ∫ ...

Question

Evaluate:
$\int (log (l o g x) + \frac{1}{(log x)}) d x$

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Solution

Now,
$\int (log (l o g x) + \frac{1}{(log x)}) d x$
$= \int (log (l o g x)) +$ $\int (\frac{1}{(log x)}) d x$
$= x log (log x)$ $- \int (\frac{1}{(log x)}) d x$ $+ \int (\frac{1}{(log x)}) d x$ { Using integration by parts]
$= x log (log x) + c$ [ Where $c$ is integrating constant]

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