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Homework Help: Integration strategy?

  1. Sep 21, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]\int[/tex][tex]\frac{\frac{1}{3}x+\frac{2}{3}}{x^{2}-x+1}[/tex]


    2. Relevant equations

    This is the result of a partial fraction integration. I don't think a direct u-substitution will work or an integration by parts.

    3. The attempt at a solution

    I don't know which I should use! We learned so many and none seem to work nicely in this case. Should I try to do a trigonometric substitution? That is my best guess, but since there is no radical I have no idea how to implement it!

    Any sort of hint would be great. I'm just not "seeing it" ;)
     
    Last edited: Sep 21, 2008
  2. jcsd
  3. Sep 21, 2008 #2

    Defennder

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    Homework Helper

    Complete the square of the denominator then break it up using (a+b)(a-b) = a^2 - b^2. From here you can do it by partial fractions, though it appears tedious.
     
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