what is the integration of integral
$$\int\cot(\log(\sin(x))\, dx$$
I have tried:
Let $\log(\sin(x))=z$ or $\dfrac{1}{\sin(x)}\cos(x)\cdot dx=dz$ , that means $\cot(x)\cdot dx=dz$ $\Longrightarrow$ integration of $dz$ is $z$ then $c=\dfrac{\log(\sin(x))^2}{2}c$ is it true?
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