calculus - Integrating cos and csc

$$\int{\frac{\sqrt{\cos x+1}}{\csc x}dx}$$
Sorry for the bad formatting, I still need to learn math jax. I am trying to integrate this by u-sub but am stuck. Looking at the equation I can see somewhere I will probably have to use the fact the $\csc x=1/\sin x$. My hunch is I choose $u$ to be something in the numerator, but is there an identity i'm not seeing?

Answer

Guide:

$$\begin{align} \int \frac{(\cos x+1)^\frac12}{ \csc x} \, dx = \int \sin x(\cos x+1)^\frac12 \, dx \end{align}$$

Try substitution $u = \cos x + 1$.