Evaluate: `int(sinx)/(1+sinx)\ dx`

Explanation

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

### Step 1: Multiply by the Conjugate
We start by multiplying the numerator and denominator by the conjugate of the denominator, which is \( 1 - \sin x \):

\[ \int \frac{\sin x}{1 + \sin x} \, dx = \int \frac{\sin x (1 - \sin x)}{(1 + \sin x)(1 - \sin x)} \, dx \]
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