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Partial fractions

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data

    We were given a worksheet to integrate some problems using partial fractions. This one however I cannot figure out what to do with it. This is the problem.

    ∫(x3-4x2+x+6)/(x2-x+2) dx

    3. The attempt at a solution

    using long division i got ∫(x-3) (-4(x-3)/(x2-x+2) dx
    split it up into ∫xdx - 3∫dx - 4∫(x-3)/(x2-x+2)
    now I don't know what to do with the x2-x+2?
    any suggestions on how to proceed from here? Thanks in advance!
     
  2. jcsd
  3. Mar 11, 2012 #2

    SammyS

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    What you have done so far looks correct.

    For the integral [itex]\displaystyle \int 2\frac{2x-6}{x^2-x+2}\,dx\,,[/itex] notice that the derivative of the denominator is 2x-1.

    Split the integrand up into [itex]\displaystyle
    2\frac{2x-1}{x^2-x+2}+2\frac{-5}{x^2-x+2}\,.[/itex]

    So you get two integrals. The first results in a logarithm. For the second one, complete the square in the denominator.
     
  4. Mar 11, 2012 #3
    So I'm allowed to multiple the integrand by 2?
     
  5. Mar 11, 2012 #4
    thank you
     
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