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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $\int \large\frac{1}{x \log _e x \log ( \log _e x)}$$ dx$

\[\begin {array} {1 1} (a)\;\log_e | \log (\log _e x)|+c\\ (b)\;| \log (\log _e x)|+c \\ (c)\;\log \log_e | \log (\log _e x)|+c \\ (d)\;x^2 +c \end {array}\]

1 Answer

$\log (\log_e x)=t$
differentiate with x
$\large\frac{1}{\log _e (x)} \times \frac{1}{x} $$.dx=dt$
By putting values
$\int \large\frac{1}{t} $$dt$
=> $ \log_e |t| +c$
=>$\log_e | \log (\log _e x)|+c$
Hence a is the correct answer.
answered Dec 21, 2013 by meena.p
 
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