# How to calculate definite integral when boundary is a limit?

Integrate[Log[x]/(1-x)^2,{x,eta,Infinity}]


The conditions are eta>0, and eta->1, how to incorporate the conditions?

• If you want to integrate along a continuous path, going clockwise halfway round the pole at x = 1, then evaluate Assuming[0 < eta < 1 && 0 < eps < 1 - eta, Integrate[Log[x]/(1 - x)^2, {x, eta, 1 - eps, 1 + I eps, 1 + eps, Infinity}] // Simplify]. Use 1 - I eps to go anticlockwise halfway round the pole. – Stephen Luttrell Jun 13 '14 at 9:00
• @DanielLichtblau Please consider posting an answer :) – Kuba Jun 19 '14 at 8:30

Use Assumptions (as per documentation).
ii = Integrate[Log[x]/(1 - x)^2, {x, eta, Infinity},