Trouble finding inverse of a function

I have the following Mathematica code:

f[U_] = 1 - (Un/U)^3; Un = 1;L[Us_] := 3 NIntegrate[   Us^(5/2)/U^(3/2) Sqrt[f[Us]/f[U]] 1/    Sqrt[U^5 f[U] - Us^5 f[Us]], {U, Us, Infinity}]UsvsL = Table[{Us, L[Us]}, {Us, 1.01, 2.01, 0.01}]

I am trying to find Us as a function of L or Us[L], for which I tried InverseSeries:

l[Us_] =  Integrate[  Series[Us^(5/2)/U^(3/2) Sqrt[f[Us]/f[U]] 1/    Sqrt[U^5 f[U] - Us^5 f[Us]], {U, 0, 4}], U]Us1 = InverseSeries[l[Us], l] // PowerExpand // Simplify 

but, to no avail. I need a table of LvsUs where I can vary the L values to obtain the corresponding Us values. Any help in this regard would be truly beneficial!