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Partial fraction

  1. Apr 24, 2012 #1
    Hi guys I have a question here relating integration by partial praction..


    the question said what is the antiderivative of

    x^2+2x-1/2x^3 +3x^2 - 2x

    valid only when x > 1/2.

    anyway i had poor background in math and working hard to catch up...
    I dont understant why "valid only when x > 1/2".
    if you integrate that indefinte integral when do you have to do to make sure relate x>1/2
     
  2. jcsd
  3. Apr 24, 2012 #2
    While the function certainly exists for many points less than 1/2, it is not continuous over the interval -inf<x<1/2 since it has three singularities (I'll let you solve for these). Thus it is best to define the domain of the function as 1/2<x<inf. Now as for the integration by partial fraction, try solving this equation for A, B and C by setting x to certain values(in order to eliminate only A, B or C):

    [tex]\frac{x^{2}+2x-1}{2x^{3}+3x^{2}-2x}=\frac{A}{x}+\frac{B}{x+2}+\frac{C}{2x-1}[/tex]

    Then you'll be able to integrate.
     
  4. Apr 24, 2012 #3
    hey thank you so much.
    you explain it better than what I thought


    great work !
     
  5. Apr 24, 2012 #4
    Anytime man, I appreciate the feedback.
     
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