NIntegrate[e^(-x) ((1 + 2 x)/(1)) (BesselK[0, 2 Sqrt[x] Sqrt[1+x]]+BesselK[2, 2 Sqrt[x] Sqrt[1 + x]]) + (4 x^2 +2 x-1)*BesselK[1, 2 Sqrt[x] Sqrt[1+x]]*e^(-x)/((1)Sqrt[x] Sqrt[1 + x]),{x,0,1}