I have two functions which are the linear and non-linear solution of an equation. I'm trying to calculate where does the linear solution is a good solution of my equation, when compared with the non-linear. To do so I am using 
[![Formula used][1]][1]
  [1]: https://i.sstatic.net/KCLED.png

The variables I'm using are

    T = 298.15(*K*);
    k1 = 1.38064852*10^-23 (*J/K*);
    \[Epsilon]0 = 8.85418781761*10^-12 (*C^2/N m^2||F/m||C/V m*);
    \[Epsilon] = 78.5;
    \[Epsilon]R = \[Epsilon] \[Epsilon]0 (*C^2/N m^2||F/m||C/Vm*);
    c = 2.99792458*10^8(*m/s*);
    z = 1;
    e1 = 1.60217733*10^-19 (*C*);
    NA = 6.022140857*10^23 (*mol^-1*);
    a = 4.25(*\[Angstrom]*);
    a1 = a*10^-10 (*m*);
    x1 = x*10^-10 (*m*);
And the main code is

    nMKS[\[Rho]0_] = \[Rho]0 *10^3 NA (*m^-3*);
    \[Kappa]MKS[\[Rho]0_] = Sqrt[(
      2 nMKS[\[Rho]0] (e1^2) (z^2) )/(\[Epsilon]R k1 T)](*m^-1*);
    L\[Sigma]MMKS[\[Rho]0_, \[Psi]H_] = \[Epsilon]R \[Kappa]MKS[\[Rho]0] \
    \[Psi]H/1000  (*C/m^2*);
    L\[Psi]PBMKS[\[Rho]0_, \[Psi]H_, 
       x_] = \[Psi]H Exp[\[Kappa]MKS[\[Rho]0] (a1/2 - x1)] (*mV*);
    L\[Sigma]MKS[\[Rho]0_, \[Psi]H_, x_] = 
      Piecewise[{{0, 
         0 <= x1 < a1/
          2}, {\[Epsilon]R \[Kappa]MKS[\[Rho]0] L\[Psi]PBMKS[\[Rho]0, \
    \[Psi]H, x]/1000, x1 >= a1/2}}](*C/m^2*);
    NL\[Sigma]MMKS[\[Rho]0_, \[Psi]H_] = (
       2 \[Epsilon]R \[Kappa]MKS[\[Rho]0] k1 T)/( z e1)
        Sinh[(z e1 )/(2 k1 T) \[Psi]H/1000] (*C/m^2*);
    ZMKS[\[Psi]H_] = (z e1 \[Psi]H/1000)/(2 k1 T);
    NL\[Sigma]MKS[\[Rho]0_, \[Psi]H_, x_] = 
      Piecewise[{{0, 
         0 <= x1 < a1/2}, {(4 \[Epsilon]R \[Kappa]MKS[\[Rho]0] k1 T)/( 
          z e1) (((Exp[2 ZMKS[\[Psi]H]] - 
                1) Exp[\[Kappa]MKS[\[Rho]0] (a1/2 - x1)])/((Exp[
                 ZMKS[\[Psi]H]] + 
                1)^2 - ((Exp[ZMKS[\[Psi]H]] - 
                  1) Exp[\[Kappa]MKS[\[Rho]0] (a1/2 - x1)])^2)), 
         x1 >= a1/2}}](*C/m^2*);
Hence, when I try to integrate my equation with

    Dif2\[Sigma][\[Rho]0_, \[Psi]H_, x_] = 
     FullSimplify[(NL\[Sigma]MKS[\[Rho]0, \[Psi]H, x] - 
        L\[Sigma]MKS[\[Rho]0, \[Psi]H, x])^2]
    V\[Sigma][\[Rho]0_, \[Psi]H_] = 
     FullSimplify[Sqrt[
      Integrate[Dif2\[Sigma][\[Rho]0, \[Psi]H, x], {x, a/2, Infinity}]]]
Mathematica is not able to solve it. How can I force mathematica to actually solve this and thereafter define a function from its solution? Thanks in advance.