Evaluate: 1+ 2 x d x - Vidyadip

Question

Evaluate:

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

✓

Answer

$\begin{aligned} & \int \sqrt{1+\sin 2 x} d x \\ = & \int \sqrt{\cos ^2 x+\sin ^2 x+2 \sin x \cos x} d x \\ = & \int \sqrt{(\cos x+\sin x)^2} d x \\ = & \int(\cos x+\sin x) d x \\ = & \int \cos x d x+\int \sin x d x \\ = & \sin x-\cos x+c .\end{aligned}$

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