# JEE Advanced Indefinite Integration 2

Calculus Level 5

If $\displaystyle I=\int \dfrac{dx}{\sin x \sqrt{\sin (2x+\alpha)}}$ for $0<\alpha<\dfrac{\pi}{2}$ and $f(x)=\log \left |\cot x+\cot \alpha + \sqrt{\cot^2x-\csc^2\alpha }\right |$, then find $I$.



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