Try substituting and it will reduce to a known rational integral.
THE BEST way :
we will multiply and devide into the integral .
and now from twofold we have :
and then u = 1-cosx and du = sinx and :
We have indeterminate Integral . so for |sinx| we can suppose that
and for we should multiply -1 to answer .
and we should consider the both cases when its poisitve and when its negative ..
The general case is consider the positive one ..
I think you know what I mean ..
The problem here is that I do not know how to say what I mean in English