I need help how this $I_r$ is calculated. It says residue but can any one help me to reach the final results.
2026-03-28 20:55:59.1774731359
How to calculate the Residue?
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As user2958701 we would need more information to see howe the contour integral is performed. However, what can be said is that if you have a function of the form f(z)/[z(1-z)], with f analytic in a neighborhood of z = 0 and z = 1 then the residues at z = 0 and z = 1 are f(0) and -f(1), respectively. To see this, just perform a Laurent expansion near these points.