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Use partial fractions to integrate x^3/x^3+1

  1. Jul 26, 2010 #1
    Use partial fractions to integrate x^3/(x^3+1)


    3. The attempt at a solution

    [tex]\int x^{3}/(x^{3}+1) dx[/tex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution

    [tex]\int x^{3}/x^{3}+1 dx[/tex]

    I know that first i have to perform long division but i am at a loss how to do this

    THanks
     
    Last edited: Jul 26, 2010
  2. jcsd
  3. Jul 26, 2010 #2
    You can do long division, or you can just rewrite the integrand:

    [tex] \frac{x^3}{x^3 + 1} = 1 - \frac{1}{x^3 + 1} [/tex]

    Now use partial fractions on that. Something similar comes out of long division. Then you have a big mess to slog through. The answer has two log terms and an arctan term.
     
  4. Jul 27, 2010 #3

    HallsofIvy

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    If you are wondering how hgfalling got that without doing "long division", I suspect the rewrote it as
    [tex]\frac{x^3}{x^3+ 1}= \frac{x^3+ 1- 1}{x^3+ 1}= \frac{x^3+ 1}{x^3+ 1}- \frac{1}{x+1}[/tex]
     
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