Question

Find:

`int (cos2 x)/(sin x + cos x)^2  dx`

Answer 1

Let I= `int (cos2 x)/(sin x + cos x)^2  dx`

= `int(cos^2 x - sin^2x)/(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)  dx)/(cos x + sin x)`

Put cos x + sin x = t

(−sin x + cos x) dx = dt

= `int(dt)/(t)`

= log |t| + C

= log(cos x + sin x) + C