P[J_]  :=  Exp[- J J / 2]/Sqrt[2 Pi]

I1[J_]  :=  Integrate[P[K], {K, 0, J}]

I1[J]

Integrand[J_]  := 8 P[J] I1[J] I1[J]

DeltaEm =  Integrate[Integrand[J], {J, 0, +Infinity}]