A problem by Harshil Patel

Level pending

Let \(f\) : [1,\(\infty)\) \(\Longrightarrow\) [2,\(\infty)\) be a differentiable function such that f(1)=2. If 6\(\int_1^x f(t) dt = 3xf(x) - x^{3}\) for all x\(\geq \)1, then the value of f(2) is

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