Question:
Write a value of $\int \frac{\sin x+\cos x}{\sqrt{1+\sin 2 x}} d x$
Solution:
We know that
$1+\sin 2 x=\sin ^{2} x+\cos ^{2} x+2 \sin x \cos x=(\sin x+\cos x)^{2}$
$y=\int \frac{\sin x+\cos x}{\sqrt{(\sin x+\cos x)^{2}}} d x$
$y=\int \frac{(\sin x+\cos x)}{(\sin x+\cos x)} d x$
$y=\int d x$
Use formula $\int c d x=c x$, where $c$ is constant
$y=x+c$
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