ClearAll["Global`*"]
Ri = 10.5/10^3;
Ro = 11.5/10^3;
h = 1/10^3;
c = 30/10^3;
l = 3/10^3;
[Mu] = (4*Pi)/10^7;
i0 = 1;
f = 0.159*10^9;
[Omega] = 2*Pi*f;
[Sigma] = 1;
Subscript[[CapitalLambda], 2] = Sqrt[[Gamma]^2 + I*[Omega]*[Mu]*[Sigma]];
[ScriptCapitalL] = (([Mu]*Pi)/(h*(Ri - Ro))^2)*NIntegrate[(r*BesselJ[1, [Gamma]*r])*
     (R0*BesselJ[1, [Gamma]*R0])*((1 - E^((-h)*[Gamma]))^2/(E^(2*l*[Gamma])*[Gamma]^2))*
     ((E^(2*c*[Gamma] + 2*(c + 2*h + l)*Subscript[[CapitalLambda], 2])*
       (-1 + E^(2*c*Subscript[[CapitalLambda], 2]))*([Gamma] - Subscript[[CapitalLambda], 2])*
       ([Gamma] + Subscript[[CapitalLambda], 2])*
       ((-(E^(2*(2*h + l)*[Gamma]) + E^(2*c*Subscript[[CapitalLambda], 2])))*
         ([Gamma] - Subscript[[CapitalLambda], 2])^2 +
        (1 + E^(4*h*[Gamma] + 2*l*[Gamma] + 2*c*Subscript[[CapitalLambda], 2]))*([Gamma] + Subscript[[CapitalLambda], 2])^
          2))/(E^(2*(c + 2*h + l)*([Gamma] + Subscript[[CapitalLambda], 2]))*
        ([Gamma] - Subscript[[CapitalLambda], 2])^4 +
       E^(2*(c + 2*h + l)*[Gamma] + 2*(3*c + 2*h + l)*Subscript[[CapitalLambda], 2])*
        ([Gamma] + Subscript[[CapitalLambda], 2])^4 - E^(2*c*[Gamma] + 2*(c + 2*h + l)*Subscript[[CapitalLambda], 2])*
        (2*E^(4*h*[Gamma] + 2*l*[Gamma] + 2*c*Subscript[[CapitalLambda], 2]) +
         (-1 + E^(2*c*Subscript[[CapitalLambda], 2]))^2)*([Gamma]^2 - Subscript[[CapitalLambda], 2]^2)^2)),
    {[Gamma], 0, Infinity}, {r, Ri, Ro}, {R0, Ri, Ro}]