December 29th, 2012, 06:37 PM  #1 
Newbie Joined: Jun 2012 Posts: 15 Thanks: 0  Evaluate Integral
?(x)(In(1+X^2)dx My attempt, On the link: 
December 29th, 2012, 07:05 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Evaluate Integral
I think your substitution is good: and we have: Now, use integration by parts: and we have: 
December 29th, 2012, 07:20 PM  #3  
Newbie Joined: Jun 2012 Posts: 15 Thanks: 0  Re: Evaluate Integral Quote:
 
December 29th, 2012, 07:34 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Evaluate Integral
I'm not sure what you mean, but we may look at the integral as: Since we let this means we may write: 
December 29th, 2012, 07:49 PM  #5  
Newbie Joined: Jun 2012 Posts: 15 Thanks: 0  Re: Evaluate Integral Quote:
 
December 29th, 2012, 07:59 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: Evaluate Integral
If we had then we would have the reciprocal in front of the integral to effectively be multiplying the integral by 1, so that we do not change its value. In the problem above we needed a 2 with the x to get the differential, so we countered with a 1/2 in front.


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