Can this integral be approached in a different way? Mathematica 11.2 spits out the input.
$Assumptions = p1 > 0 && Element[p1, Reals]
$Assumptions = p4 > 0 && Element[p4, Reals]
$Assumptions = p5 > 0 && Element[p5, Reals]
$Assumptions = r1 > 0 && Element[r1, Reals]
Integrate[Pi*(Sin[p1*r1]/(p1*r1))*((Log[(p1 - p3)^2/(p1 + p3)^2]*Log[(p1 - p4)^2/(p1 + p4)^2])/(p3*p4)), {p1, a, b}]
(* Integrate[(Pi*Log[(p1 - p3)^2/(p1 + p3)^2]*Log[(p1 - p4)^2/(p1 + p4)^2]*Sin[p1*r1])/(p1*p3*p4*r1), {p1, a, b}]*)