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Question
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
Solution
Let `I = int (cos 2x)/((cos x + sin x)^2)`
`= int (cos^2 x - sin^2 x)/((cos x + sin x)^2) dx`
`= int ((cos x - sin x) (cos x + sin x))/(cos x + sin x)^2 dx`
`= int (cos x - sin x)/(cos x + sin x) dx`
Put `cos x + sin x = t`
`(- sin x + cos x) dx = dt`
`therefore I = int dt/t = log abs t + C`
`= log abs (cos x + sin x) + C`
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