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Partial Fraction Problem

  1. Feb 25, 2014 #1
    1. The problem statement, all variables and given/known data
    ∫(5x2+20x+6)/(x3+2x2+x


    2. Relevant equations



    3. The attempt at a solution
    (5x2+20x+6)/(x3+(x(x2+2x+1)

    (5x2+20x+6)=(A/x)+(B/(x+1))+(C/(x+1))

    (5x2+20x+6)=x2(A+B+C)+x(2A+B+C)+A

    5=A+B+C
    20=2A+B+C
    6=A

    It's not coming out quite right. Did I maybe factor the denominator incorrectly?
     
  2. jcsd
  3. Feb 25, 2014 #2

    LCKurtz

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    You want$$
    \frac{5x^2+20x+6}{x(x+1)^2}=\frac A x + \frac{Bx+C}{(x+1)^2}$$
     
  4. Feb 25, 2014 #3
    Ohh! But wouldn't you need one for x+1?:

    A/x + (Bx+C)/(x+1)2 + (Dx+E)/(x+1)
     
  5. Feb 25, 2014 #4

    Dick

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    No, you only need three independent variables. You could write it as $$\frac A x + \frac{Bx+C}{(x+1)^2}$$ as LCKurtz did, or you could write it as $$\frac A x + \frac{B}{(x+1)^2}+\frac{C}{(x+1)}$$.
     
  6. Feb 25, 2014 #5
    Oh ok! Thanks for clearing that up :)
     
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