I have to find the function $\rho(r)$ that extremizes the functional $F$:
A = (Log - 1)/(2 Pi^2); b = 20.4562557; rs[r_] := (3/(4 Pi \[Rho][r]))^(1/3); F = 2.84 \[Rho][r]^(5/3) + (-(3/4) (3/Pi)^(1/3) \[Rho][r]^(1/3) + A*Log[b/rs[r] + b/rs[r]^2 + 1]) \[Rho][r] - 79/r \[Rho][r];
under the condition that $\int\rho(r)dr=79$.
I read the documentation, but it seems not really helpful in this case, since I do not know in advance the functional form of $\rho(r)$.
How can I solve this problem?