Question

Write a value of\[\int\frac{\cos x}{\sin x \log \sin x} dx\]

 

Answer 1

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