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 $x=4$ .