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Integral I'm stuck on

  1. Jan 5, 2012 #1
    1. The problem statement, all variables and given/known data

    [tex]∫x^2/(x^2+4x+8)dx[/tex]

    2. Relevant equations

    N/A

    3. The attempt at a solution

    I've tried a few things so far and nothing clicked, I may be just missing something obvious ... if anybody sees the solution and could just give me the first step or a hint, that would be sweet ... this isn't for homework or a class or anything, just a HUGE list of integrals that was given to me a month or so ago via a kind sir on this forum so I could do a few integrals each day for practice. This one (pretty sure) was on the 2nd page of the list and I'm now on the 4th page, but it has been on a little post-it for the last two weeks since I haven't been able to figure it out as I kept going through the rest of the list.

    Any help is appreciated.
     
  2. jcsd
  3. Jan 5, 2012 #2

    Mark44

    Staff: Mentor

    x2/(x2 + 4x + 8) is an improper rational function. I would start by using polynomial long division to rewrite the integrand as 1 + <proper rational function>.
     
  4. Jan 5, 2012 #3
    thanks, got it within 2 minutes of reading that ... knew I was just missing something simple.

    x + ln(x^2+4x+8) + c
     
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