Evaluate the integral \[ I=\int _0^\infty \frac {x^\alpha \,dx}{(x-1)^2+1}. \] (where \(\alpha \) is a constant, such that the integral converges: \(|\alpha |<1\)).
Question
Math 6420 • PDE
Fall 2006 • Question 9
Question
Fall 2006 • Question 9
Evaluate the integral \[ I=\int _0^\infty \frac {x^\alpha \,dx}{(x-1)^2+1}. \] (where \(\alpha \) is a constant, such that the integral converges: \(|\alpha |<1\)).