Mathematics

$$\displaystyle \int \frac{cosec x}{\log \tan \left ( x/2 \right )}dx$$


ANSWER

$$\displaystyle \log \left [ \log \tan \left ( x/2 \right ) \right ].$$


SOLUTION
Let $$\displaystyle I=\int \frac{cosec x}{\log \tan \left ( x/2 \right )}dx$$
Put $$ \displaystyle \log  \tan  \left( x/2 \right) =t\Rightarrow \cos  \sec  xdx=dt$$
Therefore 
$$ \displaystyle I=\int { \frac { dt }{ t }  } =\log { t } =\log  \left[ \log  \tan  \left( x/2 \right)  \right] $$
Hence, option 'A' is correct.
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