int frac{sin x + cos x}{sqrt{1 + sin 2x}} , d | vedclass

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(C) Given integral: $I = \int \frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} \, dx$ Since $1 + \sin 2x = \sin^2 x + \cos^2 x + 2 \sin x \cos x = (\sin x +

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$x + c$

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(C) Given integral: $I = \int \frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} \, dx$ Since $1 + \sin 2x = \sin^2 x + \cos^2 x + 2 \sin x \cos x = (\sin x + \cos x)^2$,Substituting this into the integral: $I = \int \frac{\sin x + \cos x}{\sqrt{(\sin x + \cos x)^2}} \, dx$ $I = \int \frac{\sin x + \cos x}{\sin x + \cos x} \, dx$ $I = \int 1 \, dx = x + c$ Thus,the correct option is $C$.

$\int \frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} \, dx = $

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