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Tricky Intregral

  1. Dec 21, 2009 #1
    1. The problem statement, all variables and given/known data
    Okay, here's the problem: integrate ((x^3) - 1) / ((x^3) + x) dx

    2. Relevant equations
    What is the solution and the method?

    3. The attempt at a solution
    I know this involves partial fractions, which I attempted to no avail, since the numerator is the same degree as the denominator. I even factored the numerator into (x - 1)((x^2) + x + 1), but I can't seem to figure out what to do.
  2. jcsd
  3. Dec 21, 2009 #2


    User Avatar
    Homework Helper

    [tex]\int \frac{x^3 - 1}{x^3 + x}\mathrm{d}x[/tex]
    If factoring doesn't help, I'd try splitting it into a sum of two integrals.

    If you're really stuck, mouseover this for a clue:
    x^3 - 1 = (x^3 + x) - (x + 1)
    Last edited: Dec 21, 2009
  4. Dec 21, 2009 #3


    Staff: Mentor

    Or you can simply divide the numerator by the denominator using polynomial division.
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