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The physical significance of the results are not very clear, can anyone explain it?

1. The problem statement In calculating the amplitude for the diagram[1], view 1.jpg. [1] Voja Radovanovic, Problem Book Quantum Field Theory 2. Homework Equations View 2.jpg. The Attempt at a Solution View 3.jpg.[/B] Why the integrals is divergent? Why the other terms are finite?