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Integration of a fraction

  1. Jan 3, 2012 #1
    1. The problem statement, all variables and given/known data

    ∫(1/(x^2-x+1)dx

    2. Relevant equations

    No idea


    3. The attempt at a solution

    I tried this by the subsitution method but that attempt was feeble as it only complicated the integral even further.
    let t=x^2-x+1

    this integral can neither be split into partial fractions.

    I have no idea how to proceed forward.
     
  2. jcsd
  3. Jan 3, 2012 #2

    phyzguy

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    Science Advisor

    Write (x^2 - x +1) as (x-1/2)^2 +3/4. Then make the substitution u=x-1/2. Now the integrand is in the form of 1/(u^2 + a^2), which hopefully you know how to do with a trigonometric substitution.
     
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