Appendix for Hw3, III.2.  Relevant integrals.

ClearAll[m, px, q, wp, n, i, e]

$Assumptions = m > 0 && q > 0 && a > 0;
wp = Sqrt[ a^2 + m^2 + px^2];
n = Integrate[ (1/(2wp))( 1/(wp Sqrt[m^2 + q^2] - px q) -1/(wp m) )^2, {px, -Infinity, Infinity}] // FullSimplify;
n // TraditionalForm
e = Integrate[ (1/(2))( 1/(wp Sqrt[m^2 + q^2] - px q) -1/(wp m) )^2, {px, -Infinity, Infinity}] // FullSimplify;
e // TraditionalForm

Integrate[ 1/(x^2 + y^2), {x, -Infinity, Infinity}, {y, -Infinity, Infinity}]
Integrate[ 1/Sqrt[x^2 + y^2], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}]

Integrate[ 1/(x^2 + y^2), {x, -a, a}, {y, -a, a}]
Integrate[ 1/Sqrt[x^2 + y^2], {x, -a, a}, {y, -a, a}] // FullSimplify

ArcSinh[1]// N