`intsinxsqrt(1+cos2x)\ dx`

Explanation

To solve the integral \( \int \sin x \sqrt{1 + \cos 2x} \, dx \), we will follow these steps:

### Step 1: Simplify the expression under the square root
We know that:
\[ \cos 2x = 2\cos^2 x - 1 \]
Thus, we can rewrite \( 1 + \cos 2x \) as:
...