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"Partial Fractions" Decomposition Integrals

  1. Jul 10, 2015 #1
    Hello,

    I was just introduced to this concept and I have solved a few problems, but I haven't come across any with denominators to a raised power yet.

    ∫ 1 / [(x+7)(x^2+4)] dx

    I would appreciate any directed help.

    1. from the initial state I have broken the fraction into two assuming that (x+7)(x^2+4) is the common denominator where A and B are unknown.

    ∫ A / (x+7) + B / (x^2+4)

    B / (x^2+4) has me confused

    as I said before, I have not come across denominators to a raised power before and understand that the numerator needs to be raised to one power less, but what this looks like I don't know.
     
  2. jcsd
  3. Jul 10, 2015 #2

    SteamKing

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    The first part of your PF decomp, A / (x + 7), is OK. For the second part, B / (x2 + 4), you should assume the numerator is a polynomial one-degree lower than the denominator, which is why you assume A / (x + 7).

    For the second part, instead of just B in the numerator, what should you assume?
     
  4. Jul 10, 2015 #3
    Bx + B + 1?
     
  5. Jul 10, 2015 #4

    SteamKing

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    And why would you assume this?
     
  6. Jul 10, 2015 #5
    because the polynomial on the bottom is in degrees of x so B ( x + 1 ) is better?
     
  7. Jul 10, 2015 #6

    SteamKing

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    You're assuming that the coefficient of x and the constant will be the same. That's a bad assumption.
    Make the numerator the more general Bx + C to cover all possibilities.
     
  8. Jul 10, 2015 #7
    ah I see now thank you for your help : )
     
  9. Jul 10, 2015 #8

    HallsofIvy

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    "In degrees of x"? Surely you meant to say "second degree in x"!
     
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