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Integration by Partial Fractions

  1. Mar 4, 2014 #1
    1. The problem statement, all variables and given/known data

    1/ (x+8)(x^2+16)
    Find the integral



    2. Relevant equations

    I keep getting this question wrong. Can someone check my steps?

    3. The attempt at a solution

    I set it up as
    A/(x+8) + (Bx+C)/(x^2+16)

    So I did, A(x^2+16)+ (Bx+C)(x+8)
    and I did that and got
    A+b=0
    8B+C=0
    16A+8C=1

    By algebra, I solved for A, B, and C and got
    A= 1/10
    B= -1/10
    C= 4/5

    So I got 1/10ln(x+8) - 1/10∫x/(x^2+16) + 4/5∫1/(x^2+16)
    and solving that out, I get 1/10ln(x+8) -1/20ln(x^2+16) + 1/5arctan(x/4)
    which is not correct.
    Where did I go wrong?
    Thanks in advance.
     
  2. jcsd
  3. Mar 4, 2014 #2

    vela

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    The linear equations A, B, and C satisfy are fine, but you didn't solve for A, B, and C correctly. If you plug in your values for A and C into the last equation, you'll see it's not satisfied.
     
  4. Mar 4, 2014 #3
    Oh I see my mistake. Such a simple error. Thank you.
     
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