\int \frac{\sin x+\cos x}{\sqrt{1+\sin 2 x}} d x= ?
(A) x+k
(B) 2 x+k
(C) 2 x-k
(D) 3 x+k
\int \frac{\sin x+\cos x}{\sqrt{1+\sin 2 x}} d x= ?
(A) x+k
(B) 2 x+k
(C) 2 x-k
(D) 3 x+k

The correct option is (A) x+k

    \[\begin{aligned} & \frac{(\sin x+\cos x) \cdot d x}{\sqrt{1+\sin 2 x}} \\ =& \frac{(\sin x+\cos x) \cdot d x}{\sqrt{(\sin x+\cos x)^{2}}} \\ =& \frac{(\sin x+\cos x) \cdot d x}{\sin x+\cos x} \\ =& \int d x \\ =& x+k \end{aligned}\]