Evaluate `int1/(1-sin(x/2))dx`

Explanation

To evaluate the integral \( \int \frac{1}{1 - \sin\left(\frac{x}{2}\right)} \, dx \), we can follow these steps:

### Step 1: Multiply and Divide by \( 1 + \sin\left(\frac{x}{2}\right) \)
We start by multiplying and dividing the integrand by \( 1 + \sin\left(\frac{x}{2}\right) \):

\[ \int \frac{1}{1 - \sin\left(\frac{x}{2}\right)} \, dx = \int \frac{1 + \sin\left(\frac{x}{2}\right)}{(1 - \sin\left(\frac{x}{2}\right))(1 + \sin\left(\frac{x}{2}\right))} \, dx \]
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