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Homework Help: Partial Fractions problem not matching Wolfram Alpha

  1. May 19, 2012 #1
    1. The problem statement, all variables and given/known data
    ∫10x-2x2/((x-1)2(x+3))

    Solve by partial fractions.

    3. The attempt at a solution

    ∫A/(x-1) +B/(x-1)2 + C(x+3)

    after setting up the partial fractions and multiplying each term by LCD:

    10x-2x2= A(x-1)(x+3) + B(x+3) + C(x-1)2

    10x-2x2= A(x2+2x-3) +Bx+3B +Cx-C

    10x-2x2= Ax2+2Ax-3A+Bx+3B+Cx-C

    10x-2x2= x2(A+C) +x(2A+B-2C) + (3B+C-3A)

    System of Equations:

    A+C = -2
    2A+B-2C=10
    3B+C-3A =0

    Solving these, I get A=23. B=14. C=25.

    Putting them back in their partial fractions form and integrating I get:

    23*lnlx-1l - 14/(x-1) + 25*lnlx+3l

    However Wolfram gives me essentially the same terms but different coefficients: http://www.wolframalpha.com/input/?i=integral+of+%2810x-2x%5E2%29%2F%28%28x-1%29%5E2*%28x%2B3%29%29

    What am I doing wrong???
     
  2. jcsd
  3. May 19, 2012 #2

    vela

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    Staff Emeritus
    Science Advisor
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    You're not solving for A, B, and C correctly. Your equations are fine, but your numerical answers are not. You can easily see this by plugging the results you got for A and C into the first equation.
     
  4. May 19, 2012 #3
    THANK YOU! Got the right answer now. Algebra...a slippery fooler.
     
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