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Integrate : $\int \limits _0^{\frac{\pi}{4}} \large\frac{\sec x cosec x}{\log (\tan x)}$$dx$

\[\begin {array} {1 1} (a)\;0 \\ (b)\;1 \\ (c)\;Not defined \\ (d)\;None\end {array}\]

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1 Answer

$\log (\tan x)=t$
$\large\frac{1}{\tan x} .$$ \sec^2 x dx=dt$
$\sec x. \sec x cosec x dx=dt$
=>$\int \limits_{\infty}^0 \large\frac{\sec^2 x}{\tan n \log (\tan x)}$
=> $\int \limits _{\infty}^0 \large\frac{dt}{t}$
=> $ [\log z]_{\infty}^0$
Not defined
Hence c is the correct answer.
answered Dec 17, 2013 by meena.p