_ ^ dx x + x x = - Vidyadip

MCQ

$\int_{}^{} {\frac{{dx}}{{x + x\log x}} = } $

✓
$\log (1 + \log x)$
B
$\log \log (1 + \log x)$
C
$\log x + \log (\log x)$
D
None of these

✓

Answer

Correct option: A.

$\log (1 + \log x)$

a
(a)$\int_{}^{} {\frac{{dx}}{{x + x\,\,\log x}}} = \int_{}^{} {\frac{{dx}}{{x(1 + \log x)}}} $Now putting $1 + \log x = t \Rightarrow \frac{1}{x}\,dx = dt,$ it reduces to$\int_{}^{} {\frac{{dt}}{t}} = \log (t) = \log (1 + \log x)$.

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