Intergration coty/(log2siny)^dy?

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Answer 1 · 2018-07-27T13:45:38

#-\frac{1}{(n-1)(\log(2\sin y))^{n-1}}+C#

Let #\log(2\sin y)=t\implies \frac{1}{2\siny }(2\cosy)dy=dt\ \ or\ \ \ cot y dy=dt#

#\therefore \int \frac{\cot y}{(\log(2\sin y))^n}\ dy#

#=\int \frac{dt}{t^n}#

#=\int t^{-n}\ dt#

#=\frac{t^{-n+1}}{-n+1}+C#

#=-\frac{1}{(n-1)t^{n-1}}+C#

#=-\frac{1}{(n-1)(\log(2\sin y))^{n-1}}+C#