Find f if $\int_0^1 f(x)^2dx=\int_0^1 f(x)^3dx =\int_0^1 f(x)^4dx$
Solve these functional equations: $\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$