Step 1 :The question is asking to express the limit of the sum as a definite integral. The limit of the sum is a Riemann sum which is the definition of a definite integral.
Step 2 :The function inside the sum is \(f(x) = \frac{x}{x^2 + 1}\) and the interval is [1, 8].
Step 3 :Therefore, the limit of the sum can be expressed as the definite integral of \(f(x)\) from 1 to 8.
Step 4 :The definite integral of the function on the interval [1, 8] is \(\boxed{-\frac{\log(2)}{2} + \frac{\log(65)}{2}}\).