Evaluate: `intsqrt(cos e cx-1)dx`

Explanation

To evaluate the integral \( \int \sqrt{\cos x - 1} \, dx \), we will follow a systematic approach.

### Step 1: Rewrite the integrand
We start with the expression inside the square root:
\[ \cos x - 1 = - (1 - \cos x) = - (2 \sin^2(\frac{x}{2})). \]
Thus, we can rewrite the integral as:
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