Mathematics

$$\displaystyle \int \frac{\cot x}{\log \sin x}dx.$$


ANSWER

$$\displaystyle\log \left ( \log \sin x \right )$$


SOLUTION
Let $$ \displaystyle I=\int  \frac { \cot  x }{ \log  \sin  x } dx$$
Put $$ \displaystyle \log  \sin  x=t\Rightarrow \cot  xdx=dt$$
$$ \displaystyle I=\int  \frac { dt }{ t } =\log  t=\log  \left( \log  \sin  x \right) $$
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Single Correct Medium Published on 17th 09, 2020
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