Find the area out of the functional

Calculus Level 3

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

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