Differential Equations

Let \(f:[1,\infty ) \to [2,\infty )\) be a differentiable function such that \(f(1) = 2\). If \(6\int\limits_1^x {f(t)dt = 3xf(x) - {x^3} - 5}\) for all \(x \ge 1\), then the value of f(2) is ___________.