Trigonometric integral problem

Homework Statement

$$\int\frac{1+\sqrt{cosx}}{sinx}$$ Hi , I really need a help for this

The Attempt at a Solution

$$\int\frac{1+\sqrt{cosx}}{\sqrt{sin}\sqrt{sin}}$$

$$\int\frac{1}{sinx}$$ + $$\int\frac{1}{\sqrt{sinx}}\sqrt{}\frac{cosx}{sinx}$$ =

$$\int cscx$$ + $$\int\sqrt{cscx cotx}$$ = ?

$$\int cscx$$ is alright but i have no idea for second part .

do you have any idea ?

Make the substitution $$\sqrt{cosx}=a$$ Then simplify the resulting expression, use partial fractions and you're done.