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 Complex Analysis Complex Analysis Math Forum

 January 20th, 2010, 08:49 PM #1 Newbie   Joined: Jan 2010 Posts: 1 Thanks: 0 how to support this step mathematically Here is a problem which uses the residue theorem to evaluate a real-valued integral. evaluate the integral from 0 to infinity of In(x^2+1)/(x^2+1) dx I basically understand the solution to this integral given in the book. The book uses a semi-circle as a contour in the upper-half plane. But, the first step of the solution confuses me. This is the first step of the book's solution. step 1: let f(z)=In(z+i)/(z^2+1) I know that there is a simple pole of z=i in the upper-half plane. If I let g(z)=In(z^2+1)/(z^2+1) instead, I realize that the function will diverge when you determine the residue at z=i since In(z^2+1) goes to infinity as z tends to i. I think this probably explains why the book removes the factor (z-i) from the natural logarithm in the numerator of f(z) to prevent the function f(z) from blowing up at z=i. Is there a stronger argument to prove that we need to drop the factor (z-i) from the natural logarithm in the numerator of f(z)? Please help. Thanks. Tags mathematically, step, support Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post dalo Math Software 1 March 17th, 2013 10:19 PM iamdaniel Academic Guidance 3 February 2nd, 2012 08:42 PM Weiler Differential Equations 1 January 31st, 2012 07:15 AM robtor Applied Math 0 November 2nd, 2010 03:32 PM falcon Algebra 3 December 11th, 2009 03:44 PM

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