
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 realvalued 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 semicircle as a contour in the upperhalf 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 upperhalf 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 (zi) 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 (zi) from the natural logarithm in the numerator of f(z)? Please help. Thanks. 

Tags 
mathematically, step, support 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Matamicus  a math stepbystep problem solver  dalo  Math Software  1  March 17th, 2013 10:19 PM 
Stepbystep mathematics software/practice problems  iamdaniel  Academic Guidance  3  February 2nd, 2012 08:42 PM 
Wolfram now solves step by step differential equations!  Weiler  Differential Equations  1  January 31st, 2012 07:15 AM 
Support Vector Clustering  Finding Support Vectors  robtor  Applied Math  0  November 2nd, 2010 03:32 PM 
How can solve this simple equation please step by step  falcon  Algebra  3  December 11th, 2009 03:44 PM 