Question

\[\int\cot x \cdot \log \text{sin x dx}\]

Answer 1

\[\int\cot x \cdot \log \text{sin x dx}\]
\[Let \log \sin x = t\]
\[ \Rightarrow \frac{1}{\sin x} \times \cos x = \frac{dt}{dx}\]
\[ \Rightarrow \text{cot x dx} = dt\]
\[Now, \int\cot x \cdot \log \text{sin x dx}\]
\[ = \ ∫ t. dt\]
\[ = \frac{t^2}{2} + C\]
\[ = \frac{\left( \text{log} \left| \text{sin x }\right| \right)^2}{2} + C\]