Mathematics

$$\displaystyle \int \frac{\sec x\:co\sec x  }{\log \tan x}dx$$


ANSWER

$$\displaystyle\log \left ( \log \tan x \right ).$$


SOLUTION
Let $$\displaystyle I=\int \frac{\sec x\:cosec x  }{\log \tan x}dx$$
Put $$ \displaystyle \log  \tan  x=t\Rightarrow \sec  xcosec  xdx=dt$$
Therefore
$$ \displaystyle I=\int  \frac { dt }{ t } =\log  t=\log  \left( \log  \tan  x \right) $$
Hence, option 'C' is correct.
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Single Correct Medium Published on 17th 09, 2020
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