Help with trigonometric integral

[miglo]

Homework Statement

$$\int_{\frac{5\pi}{6}}^{\pi}\frac{\cos^{4}x}{\sqrt{1-\sin{x}}}dx$$

Homework Equations

$$\cos^{2}x=\frac{1+\cos{2x}}{2}$$

The Attempt at a Solution

i used the above equation, then expanded it all out and multiplied by the denominator and hoped i would then be able to do a simple substitution that would give me an antiderivative after integrating but that hasn't been working for me
any ideas?

 

[Hootenanny]

Homework Statement

$$\int_{\frac{5\pi}{6}}^{\pi}\frac{\cos^{4}x}{\sqrt{1-\sin{x}}}dx$$

Homework Equations

$$\cos^{2}x=\frac{1+\cos{2x}}{2}$$

The Attempt at a Solution

i used the above equation, then expanded it all out and multiplied by the denominator and hoped i would then be able to do a simple substitution that would give me an antiderivative after integrating but that hasn't been working for me
any ideas?

A relatively straightforward method involves a series of substitutions. I would start with $u=1-\sin x$