Is there a way to help Mathematica evaluate the following integral?

Integrate[((4*Log[((p1 - p3)^2 + \[Omega]^2)/((p1 + p3)^2 + \[Omega]^2)]*
     Log[((p1 - p4)^2 + \[Omega]^2)/((p1 + p4)^2 + \[Omega]^2)])/(p3*p4))*(Sin[p1]/p1), 
  {p1, 0, Infinity}, Assumptions -> Element[p1 | p3 | p4 | \[Omega], Reals], 
  Assumptions -> p1 > 0 && p3 > 0 && p4 > 0]

or alternatively

Integrate[Limit[Integrate[((4*Log[(p1 - p3 + \[Omega])/(p1 + p3 + \[Omega])]*
       Log[(p1 - p4 + \[Omega])/(p1 + p4 + \[Omega])])/(p3*p4))*(Sin[p1]/p1), {p1, 0, Infinity}, 
    Assumptions -> Element[p1 | p3 | p4, Reals]], \[Omega] -> 0], {p1, 0, Infinity}, 
  Assumptions -> Element[p1 | p3 | p4 | \[Omega], Reals]]