R = ((1 - x/L)*W^2*(16*10^-20)^2*Pi*Sqrt[me]*LnLumbda)/( T^(3/2)*e0);

Simplify[1/Sqrt[[Pi]]
   E^-S^2/(S - (W + 2 I R - Om)/(
    vt (W/CC (1 - (1 - x/L)/(1 + (Wc)/W))^(1/2))))]
-((0.5641895835477563` E^-S^2 Sqrt[
  x])/((0.016006834477809786` + 0.00008178287140291831` I) -
  1.` S Sqrt[x] - (0.` + 8.178287140291829` I) x))
A1[x_] :=
 NIntegrate[-((0.5641895835477563` E^-S^2 Sqrt[
       x])/((0.016006834477809786` + 0.00008178287140291831` I) -
       1.` S Sqrt[
        x] - (0.` + 8.178287140291829` I) x)), {S, -Infinity,
   Infinity}]
yWKB[x_] :=
 b/Sqrt[Abs[[Kappa][x]]] Exp[NIntegrate[[Kappa][xp], {xp}]]
[Kappa][x_] := Sqrt[W^2/CC^2 + (W wp^2)/(CC^2 vt k) A1[x]]
Simplify[[Kappa][x]]
Sqrt[(3.947841760435743`*^13 Sqrt[
  x] + (6.319244960388013`*^11 -
    6.319244960388012`*^16 x) NIntegrate[-((
    0.5641895835477563` E^-S^2 Sqrt[
     x])/((0.016006834477809786` + 0.00008178287140291831` I) -
     1.` S Sqrt[
      x] - (0.` +
        8.178287140291829` I) x)), {S, -[Infinity],
[Infinity]}])/Sqrt[x]]
[Kappa][x_] := [Sqrt](3.947841760435743`*^13 +
    1/Sqrt[x] (6.319244960388013`*^11 -
       6.319244960388012`*^16 x) NIntegrate[-((0.5641895835477563`
E^-S^2 Sqrt[
           x])/((0.016006834477809786` + 0.00008178287140291831` I) -
           1.` S Sqrt[
            x] - (0.` +
              8.178287140291829` I) x)), {S, -[Infinity],
[Infinity]}])
yWKB[-L]
NIntegrate::ilim
0.0004027134076113933` b E^NIntegrate[[Kappa][xp], {xp}]
Solve[0.0004027134076113933` b E^NIntegrate[[Kappa][xp], {xp}] ==
  10, b]
NIntegrate::ilim
{{b -> 24831.554676346186` E^(-1.` NIntegrate[[Kappa][xp], {xp}])}}

Plot[Abs[yWKB[x]], {x, -L, L}]