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Integrate x/(x^2 + ax + a^2)

  1. Oct 31, 2005 #1
    Hi. I want to integrate x/(x^2 + ax + a^2)
    I tried substitution with u=x^2 then du =2x but that didn't work out neither did the substitution x^2 + ax
    I thought of factorizing the denominator and using partial fractions, but I think that's not the way, can't figure out the factorization.
    Could someone please give me a hint how to integrate this.
    Last edited: Oct 31, 2005
  2. jcsd
  3. Oct 31, 2005 #2


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    Homework Helper

    If there was a 2ax in the denominator instead of ax, it would've been easier :smile:
    This is a typical example of an integral which will have an ln-part and an arctan-part. Do you see why/how?
  4. Oct 31, 2005 #3


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    Science Advisor

    TD's hint is best: complete the square!
  5. Nov 1, 2005 #4
    Compleated the square and everything works. Thanks guys.
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