Evaluate: `int1/(sqrt(1-sinx))\ dx`

Explanation

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

### Step 1: Rewrite the integrand
We start with the expression under the square root. We can use the identity \( 1 - \sin x = 1 - \sin x \cdot \frac{1 + \sin x}{1 + \sin x} = \frac{(1 - \sin x)(1 + \sin x)}{1 + \sin x} = \frac{\cos^2 x}{1 + \sin x} \).

Thus, we can rewrite the integral as:
\[
\int \frac{1}{\sqrt{1 - \sin x}} \, dx = \int \frac{1}{\sqrt{\frac{\cos^2 x}{1 + \sin x}}} \, dx = \int \frac{\sqrt{1 + \sin x}}{\cos x} \, dx
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