Question

Integrate the function $\cot x\log \sin x$

Answer 1

Put $\log \sin x=t$
$\Rightarrow \frac{1}{\sin x}\cdot \cos xdx=dt$
$\therefore \cot xdx=dt$
$\Rightarrow \int \cos x\log \sin xdx=\int tdt$
$=\frac{t^2}{2}+C$
$=\frac{1}{2}(\log \sin x{)}^2+C$