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Partial Fractions problem

  1. Apr 17, 2007 #1
    1. The problem statement, all variables and given/known data

    integrate((x^3+72)/(x^2+6x+8))dx

    2. Relevant equations



    3. The attempt at a solution

    I decided to use partial fractions method.

    x^2+6x+8 factors to (x+4)(x+2)

    x^3+72=A(x+2)+B(x+4)

    when A=-2, 64=B(2), B=32
    when B=-4, 8=A(-2), A=-4

    -4*int(1/(x+4)) + 32*int(1/(x+2))

    -4*ln(x+4) + 32*ln(x+2) <---ANSWR

    What was wrong?
     
  2. jcsd
  3. Apr 17, 2007 #2
    divide first
     
  4. Apr 18, 2007 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The numerator has higher degree than the denominator. Partial fractions only works on "proper fractions". As Mathgician said, divide first to get a polynomial plus a fraction. Then use partial fractions on that remaining fraction.
    However, that still does NOT give -4*ln(x+4) + 32*ln(x+2) as the answer: there will be a (1/2)x2- 6x part. Is it possible you've miscopied the problem?
     
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