`(cos2x-cos2alpha)/(cos x-cos alpha)`

Explanation

`int(cos 2x-cos 2alpha)/(cos x- cos alpha)dx`
`=int((2cso^(2)x-1)-(2cos^(2)alpha-1))/(cosx-cos alpha)dx`
`=int((cos^(2)x-cos^(2)alpha))/(cosx-cos alpha)dx`
`=2int(cosx+cos alpha)dx`
`=2 intcosx dx +2 cos alpha int 1dx`
`=2sin x+2xcos alpha+c`