Evaluate : `int(sinx)/(sqrt(1+sinx))dx`.

Explanation

To evaluate the integral \( \int \frac{\sin x}{\sqrt{1 + \sin x}} \, dx \), we can follow these steps:

### Step 1: Rewrite the Integral
We can manipulate the integrand by adding and subtracting 1 in the numerator:
\[ \int \frac{\sin x}{\sqrt{1 + \sin x}} \, dx = \int \frac{\sin x + 1 - 1}{\sqrt{1 + \sin x}} \, dx = \int \frac{\sin x + 1}{\sqrt{1 + \sin x}} \, dx - \int \frac{1}{\sqrt{1 + \sin x}} \, dx \]

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