w = 10^9*NIntegrate[Cos[u*x]/(1 + 10^-7*I*Sqrt[u^2 - 0.006^2])*(u*Sin[u/2])/(
u^2 - 0), {u, 0, 10^8, [Infinity]}, MaxRecursion -> 10^8]

tab1 = Table[{x, w}, {x, 1/10, 1, 1/10}];Table[{ListLinePlot[ta = Table[{x /. tab1[[i, 1]], Re[w /. tab1[[i, 2, j]]]}, {i, 1,
  20}], Epilog -> Point[ta], PlotLabel -> Re, AxesLabel -> {x, w}], ListLinePlot[ta = Table[{x /. tab1[[i, 1]], Im[w /. tab1[[i, 2, j]]]}, {i, 1,
  20}], Epilog -> Point[ta], PlotLabel -> Im,AxesLabel -> {x, w}]}, {j, 1, 1}]