# Let $I = \int {\frac{{\sin x + \cos x}}{{\sqrt {1 + \sin 2x} }}} dx = \int {\frac{{(\sin x + \cos x)}}{{\sqrt {{{\sin }^2}x + {{\cos }^2}x + 2\sin x\cos x} }}} dx$

$ = \int {\frac{{\sin x + \cos x}}{{\sqrt {{{(\sin x + \cos x)}^2}} }}} dx = \int 1 dx = x + C$