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Integration by partial fractions?

  1. Nov 14, 2012 #1
    Whoa, this here is kicking me hard! Okay, so I've got everything pretty well down until... stuff like... [tex]\int \frac{3x + 32}{x^{2}-16x + 64}dx[/tex]

    So, I get how to factor the denominator, but then what? The above won't factor... Also, I read that if the degree of the numerator is higher than the denominator I gotta do polynomial long division... I need a review of polynomial long division; Lol.
     
    Last edited by a moderator: Nov 15, 2012
  2. jcsd
  3. Nov 15, 2012 #2

    Simon Bridge

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    But the numerator is not higher order than the denominator and:$$\frac{3x + 32}{x^{2}-16x + 64}=\frac{3x+32}{(x-8)^2}$$See also:
    http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/partialfracdirectory/PartialFrac.html
     
  4. Nov 15, 2012 #3

    lurflurf

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    x^2-16x+64=(x-8)^2
    3x+32=3(x-8)+56
     
  5. Nov 15, 2012 #4

    Simon Bridge

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    ... oh yes, and complete the square in the numerator.
    Thanks lurflurf. The example does not seem to illustrate the following comments does it?
     
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