How do you integrate $(1 + \cos(x))^{5/2} dx$?

Question

I tried substituting $\cos(x) = 1 - 2\sin^2(x/2)$ but still can't figure it out. Is there any other identity to help with this integration?

Answer 1

You can use $\cos(x)=2\cos^2(\frac{x}{2})-1$ the next step can be to use $\cos^5(\frac{x}{2})=\cos(\frac{x}{2})(1-\sin^4(\frac{x}{2}))$