Đặt
x=\dfrac{\pi}{2} -t
I=\int_0^{\frac{\pi}{2}} \dfrac{\cos t}{(\sin t +\cos t)^2 }dt=\int_0^{\frac{\pi}{2}} \dfrac{\cos x}{(\sin x +\cos x)^2 }dx
\Rightarrow 2I = \int_0^{\frac{\pi}{2}} \dfrac{\sin x +\cos x}{(\sin x +\cos x)^2 }dx=\int_0^{\frac{\pi}{2}} \dfrac{1}{\sin x +\cos x }dx
=\dfrac{1}{\sqrt 2} \int \dfrac{1}{\sin (x+\dfrac{\pi}{4})}dx còn lại là vớ vẩn