April 21st, 2012, 07:50 PM  #1 
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Are there issues with this? 
April 21st, 2012, 08:12 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Are there issues with this?
I simplified your result some, then differentiated and did not get back the original integrand. That is a real bear of an integral , at least by factoring the denominator: and then using partial fraction decomposition, substitutions, etc. 
April 21st, 2012, 09:04 PM  #3  
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: Are there issues with this? Quote:
EDIT: I made a stupid mistake... Namely, Redoing and reposting, one moment. . .  
April 21st, 2012, 09:14 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Are there issues with this?
I simply looked at the suggested method given by wolframalpha.com. Your factorization of ...nevermind, I see you caught it. 
April 21st, 2012, 09:30 PM  #5 
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: Are there issues with this? How's this? 
April 21st, 2012, 09:37 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Are there issues with this?
You don't seem to actually be integrating...you should have natural logarithms in your result, i.e.,: where 
April 21st, 2012, 09:41 PM  #7 
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: Are there issues with this?
Woooooooow. facepalm This is why you never try to integrate and multitask. It works out to, instead, \lnxit+(B3B'\lnx+it+(C3C'\lnx+t+(D3D'\lnxt+C" /> Thank you for the patience, Mark. The nuances and little things are what I always miss. EDIT: The big reason I asked this topic was because I was uncertain if extending the method of partial fraction decomposition to complex numbers was a bad idea. Wolfram Alpha does not seem to like it, but it makes sense to me. 
April 21st, 2012, 09:52 PM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Are there issues with this?
Another issue: You cannot state: You need to use partial fraction decomposition. For example: With 4 linear factors in the denominator it will be more complicated. You want: 
April 21st, 2012, 10:01 PM  #9  
Senior Member Joined: Jul 2011 Posts: 245 Thanks: 0  Re: Are there issues with this? Quote:
Here are the steps: This gives us an equation: I evaluated this equation at the zeros. (it, it, t, t) This gave me the expressions for A, B, C, and D. Take A as an example:  
April 21st, 2012, 10:15 PM  #10 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Are there issues with this?
My apologies, I see that now. You are even using the coverup method. You can do a lot of simplification of your constants. For example: I find that that coefficient should be (using WA): which is simply the negative of what you have. 

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