Find the integrals of the functions $\frac{\cos2x}{(\cos x+\sin x)^2}$

Question

$\begin{array}{1 1}\log | \sin x+\cos x |+c. \\ \log | \sin x-\cos x |+c \\ \log | 2\sin x+2\cos x |+c \\ \log | 2\sin x-\cos x |+c. \end{array}$