Question

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

• A. $\left(\log \sin x\right)$
• B. $\log \left(\log \cos x\right)$
• C. $\log \frac{1}{2}\left(\log \sin x\right)$
• D. $\log \left(\log \sin x\right)$

Answer 1

The correct option is D $\log \left(\log \sin x\right)$

Let $I=\int \frac{\cot x}{\log \sin x}dx$
Put $\log \sin x=t\Rightarrow \cot xdx=dt$
$I=\int \frac{dt}{t}=\log t=\log \left(\log \sin x\right)$