$\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \dfrac{\sin x -\cos x}{\sqrt{(\sin x +\cos x)^2}}dx=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \dfrac{\sin x -\cos x}{\sin x +\cos x}dx$
Đặt $\sin x + \cos x = t \Rightarrow (\sin x -\cos x)dx = -dt$
$I=-\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \dfrac{dt}{t} =-\ln |t| \bigg |_{\frac{\pi}{4}}^{\frac{\pi}{2}}$ tự thay cận nhé