Let the function \( f : [1, \infty) \to \mathbb{R} \) be defined by
Define \( g(x) = \int_{1}^{x} f(t) dt, \ x \in (1, \infty) \). Let \( \alpha \) denote the number of solutions of the equation \( g(x) = 0 \) in the interval \( (1, 8] \) and \( \beta = \displaystyle \lim_
{x \to 1^{+}} \dfrac{g(x)}{x - 1} \). Then the value of \( \alpha + \beta \) is equal to __________.
