Evaluate: `intsqrt((x-3)(5-x))\ dx`

Explanation

To evaluate the integral \( I = \int \sqrt{(x-3)(5-x)} \, dx \), we will follow these steps:

### Step 1: Expand the expression under the square root
We start by expanding the expression inside the square root:
\[ (x-3)(5-x) = 5x - x^2 - 15 + 3x = -x^2 + 8x - 15 \]
Thus, we can rewrite the integral as:
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