Find the area out of the functional

Calculus Level 3

If \(f\) is a real-valued function such that \( f(x) \neq 0 \) for all real \(x\), and satisfies the functional equation \[\large f(x)=x\sqrt{x\sqrt{x\sqrt{x \sqrt{f(x)}}}}\] for all \(x>0\). Then find the area under the graph of \(f\) between \(x=1\) to \(x=4\).

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