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Why do I have to set up the partial fractions like this?

  1. Mar 3, 2013 #1
    1. ∫[(x4 + x + 1)/(x(x2 + 1))]dx


    2. When I first did this problem, I divided and got:
    ∫[x + (-x2 + x + 1)/(x3 + x)]dx

    (x3 + x) = x(x2 + 1)

    I then set up the fraction as: A/x + B/(x2 + 1)

    BUT, the solution to this problem says: A/x + [(Bx + C)/(x2 + 1)]

    How would I know to use Bx + C??? Where did the x come from and why do we need the C?

    Please let me know what situations need this new format.
    Thank you so much! :D
     
  2. jcsd
  3. Mar 3, 2013 #2

    rock.freak667

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    For every quadratic factor like ax^2+bx+c which cannot be expressed in terms of real solutions, the partial fractions is

    (Ax+B)/(ax^2+bx+c)
     
  4. Mar 3, 2013 #3

    Dick

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    And the reason you need it is because A/x + B/(x^2 + 1) there is no choice of A and B that will make that equal to (-x^2 + x + 1)/(x^3 + x). You really need the extra parameter.
     
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