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 .
I know it should be the absloute value ..
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