Evaluate the integral, `intsqrt(x^(2)+2x+6)dx`.

Explanation

To evaluate the integral \( \int \sqrt{x^2 + 2x + 6} \, dx \), we will follow a systematic approach involving completing the square and using a standard integral formula. Here’s a step-by-step solution:

### Step 1: Complete the square
First, we need to rewrite the expression inside the square root in a completed square form. The expression is \( x^2 + 2x + 6 \).

To complete the square:
\[
x^2 + 2x + 6 = (x^2 + 2x + 1) + 5 = (x + 1)^2 + 5
...