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Question
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
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Solution
Let `I = int ((cos 2x - cos 2alpha)/(cos x - cos alpha)) dx`
`= int ((2 cos^2 x - 1) - (2 cos^2 alpha - 1))/(cos x - cos alpha) dx`
`= int (2(cos^2 x - cos^2 alpha))/ (cos x - cos alpha) dx`
`= int ((2 cos^2 x - 1) - (2 cos^2 alpha - 1))/(cos x - cos alpha) dx`
`= 2 int (cos x + cos alpha) dx`
`= 2 int (cos x) dx + int (2 cos alpha) dx`
`= 2 sin + 2x cos alpha + C`
`= 2 (sin x + x cos alpha) + C`
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