Here I want to compute this integral, w is infinity. IF I choose w=10 Gamm[k_, u_] := 2/(15Sqrt[Pi]) N[NIntegrate[ Exp[-Iks]s^(1/2 + 2)Exp[-s]Cos[f/2] Exp[-Sqrt[8su]/Cos[f/2]], {f, -Pi, Pi}, {s, 0, w}]; Table[Gamm[0, u], {u, 0, 0.1, 0.001}] Mathematica gives: Table[Gamm[0, u], {u, 0, 0.1, 0.001}]...