Question

Integrate the function: $\cot x\log \left(\sin x\right)$

Answer 1

Given: $\int \cot x\log \left(\sin x\right).dx$
Let $\log \left(\sin x\right)=t$
Differentiating both sides w.r.t.$x$
$\frac{1}{\sin x}\cos x=\frac{dt}{dx}\Rightarrow \cot xdx=dt$
On substituting
$=\int tdt$
$=\frac{t^2}{2}+C$
$=\frac{1}{2}\left[\log \right(\sin x){]}^2+C$
Where $C$ is constant of integration