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Question
`int (cos 2x)/(sin x + cos x)^2 "d"x`
Solution
`int (cos 2x)/(sin x + cos x)^2 "d"x = int (cos^2x - sin^2x)/(cosx + sin x)^2 "d"x`
= `int ((cosx + sinx)(cosx - sinx))/(cos x + sin x)^2 "d"x`
= `int (cosx - sinx)/(cosx + sinx) "d"x`
= `log|cosx + sinx| + "c"` ........`[∵ int ("f'"(x))/("f"(x)) "d"x = log|"f"(x)| + "c"]`
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