Đáp án:

•  \( \int \frac{\cos 2x}{(\sin x + \cos x + 2)^2} \, dx = \int \frac{(\cos x - \sin x)(\cos x + \sin x)}{(\sin x + \cos x + 2)^2} \, dx \)

•  Đặt \( t = \sin x + \cos x + 2 \Rightarrow dt = (\cos x - \sin x) \, dx \)

•  \( I = \int \frac{t - 2}{t^2} \, dt = \int \left( \frac{1}{t} - \frac{2}{t^2} \right) \, dt \)

\( = \ln |t| + \frac{2}{t} + C \)