Hw3 Yukawa integral.

ClearAll[r, m, e, e2]
$Assumptions = r > 0 && m > 0 && e > 0;
e2 = Integrate[(Sinc[p r] - 1)p^2/(p^2 + m^2 - I e), {p, 0, Infinity}]

ClearAll[r, m, e]
Integrate[(Sinc[p r] - 1)p^2/(p^2 + m^2), {p, 0, Infinity}] // HoldForm// TraditionalForm
e = Integrate[(Sinc[p r] - 1)p^2/(p^2 + m^2), {p, 0, Infinity}];
Assuming[ r > 0 && m > 0, Simplify[e]]

ClearAll[r, m, e3]
e3 = -Integrate[(Sinc[p r] + 1)p^2/(p^2 + m^2), {p, 0, Infinity}];
Assuming[ r > 0 && m > 0, Simplify[e3]]

https://mathematica.stackexchange.com/questions/185981/integral-converges-only-if-mathematica-kernel-has-just-started

ClearAll[r, m, e]
e = Integrate[(Sinc[p r] - 1)p^2/(p^2 + m^2), {p, 0, Infinity}];
Assuming[ r > 0 && m > 0, Simplify[e]]

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