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Solving a polynomial integral.

  1. Dec 15, 2006 #1
    I cant seem to solve this integral,
    [tex] \int \frac{x^2+x+1}{(x^2+1)(x+1)}dx [/tex]
    Maple, however, solves is exact quiet easily, and i'd really like to see how this can be done "by hand".

    Best regards.
     
  2. jcsd
  3. Dec 15, 2006 #2
    Simplification. Integration by parts.

    http://online.math.uh.edu/HoustonACT/videocalculus/index.html

    Scroll down to number 34 and view the video for a tutorial.
     
    Last edited by a moderator: Apr 22, 2017
  4. Dec 15, 2006 #3

    arildno

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    Hmm..I hardly see how integration by parts is the simplest way of doing this.
    A much easier way is to use partial fractions decomposition.
    This is done by trying to find numbers A,B,C so that we have:
    [tex]\frac{x^{2}+x+1}{(x^{2}+1)(x+1)}=\frac{Ax+B}{x^{2}+1}+\frac{C}{x+1}[/tex]
     
    Last edited: Dec 15, 2006
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