Question
$\int \sqrt{1+\sin 2 x} d x$

Answer

$\int \sqrt{1+\sin 2 x} d x=\int \sqrt{\sin ^2 x+\cos ^2 x+2 \sin x \cos x} d x$
$=\int \sqrt{(\cos x+\sin x)^2} d x$
$=\int(\cos x+\sin x) d x$
$=\sin x -\cos x + c $

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