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Partial Fractions Calc Problem

  1. May 14, 2009 #1
    1. The problem statement, all variables and given/known data
    ∫1/[(x+a)(x+b)]dx
    answer is 1/(a-b) ln[(x+b)/(x+a)] + C


    2. Relevant equations



    3. The attempt at a solution

    1=A/(x+a) + B/(x+b)
    1=B(x+a) + A(x+b)
    1=Bx+ Ba + Ax +Ab

    so 0=Bx+ Ax, 1=Ba+Ab
    A=-B, 1=B(a-b)

    ∫-1/(x+a) +∫1/(x+b)

    Im not sure if I am headed in the right direction or not.
     
  2. jcsd
  3. May 14, 2009 #2

    gabbagabbahey

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    Gold Member

    This line should really be 1/((x+a)(x+b))=A/(x+a) + B/(x+b)

    Good, so B=___?

    This should be B∫-1/(x+a) +B∫1/(x+b)
     
  4. May 14, 2009 #3
    How do you know what A and B equal? You don't know numerical values, just what they're equal to in relation to one another.

    gabbagabbahey is right, you should get B∫-1/(x+a) +B∫1/(x+b)

    Now what do you know about the integral of 1/x ?
     
  5. May 15, 2009 #4

    HallsofIvy

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    The equation 1= B(a-b) settles that.

     
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