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Question
Solution
\[\text{ Let I }= \int \frac{\cos x}{\sin x \cdot \log \sin x}dx\]
\[ \Rightarrow \int \frac{\cot x}{\log \sin x}dx\]
\[\text{ Let log sin x} = t\]
\[ \Rightarrow \text{ cot x dx} = dt\]
\[ \therefore I = \int \frac{dt}{t}\]
\[ = \text{ log t + C}\]
\[ = \text{ log}\left( \text{ log sin x} \right) + C\]
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