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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