Rotation speed of Milky Way looks like this until about 25 kpc

I know the following points to describe this curve

{{0.1, 0.566016}, {0.11, 0.575781}, {0.121, 0.5875}, {0.133, 
  0.600781}, {0.146, 0.620703}, {0.161, 0.653906}, {0.177, 
  0.703516}, {0.195, 0.767969}, {0.214, 0.834375}, {0.236, 
  0.889844}, {0.259, 0.929297}, {0.285, 0.954688}, {0.314, 
  0.969531}, {0.345, 0.977344}, {0.38, 0.980469}, {0.418, 
  0.979297}, {0.459, 0.975391}, {0.505, 0.96875}, {0.556, 
  0.960547}, {0.612, 0.95}, {0.673, 0.936719}, {0.74, 
  0.921094}, {0.814, 0.905078}, {0.895, 0.889844}, {0.985, 
  0.876953}, {1.083, 0.866016}, {1.192, 0.855859}, {1.311, 
  0.846875}, {1.442, 0.838672}, {1.586, 0.830859}, {1.745, 
  0.823828}, {1.919, 0.818359}, {2.111, 0.814453}, {2.323, 
  0.813281}, {2.555, 0.816016}, {2.81, 0.823047}, {3.091, 
  0.833594}, {3.4, 0.848438}, {3.74, 0.867188}, {4.114, 
  0.885156}, {4.526, 0.896484}, {4.979, 0.904688}, {5.476, 
  0.914453}, {6.024, 0.926563}, {6.626, 0.935547}, {7.289, 
  0.937891}, {8.018, 0.933594}, {8.82, 0.924609}, {9.702, 
  0.916016}, {10.672, 0.914844}, {11.739, 0.926172}, {12.913, 
  0.948438}, {14.204, 0.970703}, {15.625, 0.975391}, {17.187, 
  0.961719}, {18.906, 0.950391}, {20.797, 0.952734}, {22.876, 
  0.959375}, {25.164, 0.951953}}

We could Interpolate and get an Interpolating fonction vc[R] to solve the following problem :

Knowing e=0.995, I am trying now to get the density Rho[m]from the equation

vc[R]^2 == Integrate[(4 Pi Sqrt[1 - e^2] m^2 Rho[m])/ Sqrt[-e^2 m^2 + R^2], {m, 0, R}] This equation comes from Galactic Dynamics Binney Tremaine 2008. (2.132)

But solutions given elswhere are working only with an analytical function vc[R], and I dont know why ??

Any idea ?

Thanks in advance