# 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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