_ ^ dx x x ( x) = - Vidyadip

MCQ

$\int_{}^{} {\frac{{dx}}{{x\log x\log (\log x)}} = } $

A
$2\log (\log x) + c$
✓
$\log [\log (\log x)] + c$
C
$\log (x\log x) + c$
D
None of these

✓

Answer

Correct option: B.

$\log [\log (\log x)] + c$

b
(b)$\int_{}^{} {\frac{{dx}}{{x\log x\,.\,\log (\log x)}}} $
Put $\log x = t,$ then it reduces to $\int_{}^{} {\frac{{dt}}{{t\,.\,\log (t)}}} $
Again put $\log t = z,$ then reduces form is
$\int_{}^{} {\frac{{dz}}{z}} = \log z = \log [\log (\log x)] + c$.

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