Let \( f : [1, \infty) \to [2, \infty) \) be a differentiable function. If
\( 10 \int_{1}^{x} f(t) \, dt = 5x f(x) - x^5 - 9 \) for all \( x \ge 1 \), then the value of \( f(3) \) is ______.