|x| x1 + |x| dx equals : - Vidyadip

MCQ

$\int {\frac{{\ln |x|}}{{x\sqrt {1 + \ln |x|} }}} $ $dx $ equals :

✓
$\frac{2}{3}\,\,\sqrt {1 + \ln |x|} $ $(ln|x|- 2) + c$
B
$\frac{2}{3}\,\,\sqrt {1 + \ln |x|} $ $(ln|x|+ 2) + c$
C
$\frac{1}{3}\,\,\sqrt {1 + \ln |x|} $ $(ln|x|- 2) + c$
D
$2\,\,\sqrt {1 + \ln |x|} $ $(3 ln|x|- 2) + c$

✓

Answer

Correct option: A.

$\frac{2}{3}\,\,\sqrt {1 + \ln |x|} $ $(ln|x|- 2) + c$

a
Start : $ln | x | = t$ $\Rightarrow $ $\frac{1}{x}\,dx$ = $dt$ $\Rightarrow $ $\int {\frac{{t\,dt}}{{\sqrt {1 + t} }}} $

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