(Subscript[ϕ, 1])[l,x]:= (2/l)^(1/2) Sin[Pi x /l]

ψ[l,x] := Sqrt[30] l^(-5/2) x (l - x)

N[Integrate[(Subscript[ϕ, 1])[l,x]* ψ[l,x], {x,0,l}]^2]