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Did I do this properly? Integration by Partial Fractions

  1. Mar 16, 2008 #1
    1. The problem statement, all variables and given/known data

    Evaluate the indefinite integral.

    int (6 x + 7)/(x^2 + 1) dx `

    3. The attempt at a solution

    A/(x + 1) + B/(x - 1)

    6x + 7 = A(x - 1) + B(x + 1)

    6x + 7 = (A + B)x + (-A + B)

    A + B = 6

    -A + B = 7

    A + (7 + A) = 6

    2A = -1.

    A = -.5

    B = 3.5

    So the answer should be...

    -.5ln(x + 1) + 3.5ln(x - 1) + C

    Is this correct?
     
  2. jcsd
  3. Mar 16, 2008 #2
    Differentiate your anti-derivative and see if it becomes your original Integral.

    Also, I don't think it is. How did you break ... [tex]x^2+1[/tex] ???

    You don't need to use Partial Fractions.

    [tex]\int\frac{6x+7}{x^2+1}dx[/tex]


    [tex]\int\left(\frac{6x}{x^2+1}+\frac{7}{x^2+1}\right)dx[/tex]
     
    Last edited: Mar 16, 2008
  4. Mar 16, 2008 #3
    -.5(1/x + 1) + 3.5(1/x - 1)

    Blah. =/

    What did I do wrong?
     
  5. Mar 16, 2008 #4
    Looking at your work ... looks like you broke [tex]x^2+1[/tex] to [tex](x+1)(x-1)[/tex]

    Yes?

    [tex]x^2-1=(x+1)(x-1)[/tex] so ... [tex]x^2+1\neq(x+1)(x-1)[/tex]
     
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