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Integrate f(x) = (x^3 + 3x + 12) / (x(x+2)^2)

  1. Apr 18, 2008 #1
    1. The problem statement, all variables and given/known data

    Integrate f(x) = (x^3 + 3x + 12) / (x(x+2)^2)

    2. Relevant equations

    3. The attempt at a solution

    I know that i should somehow rewrite the polynomial but I do not know how. Please, help me.
  2. jcsd
  3. Apr 18, 2008 #2
    Hmm, I don't know if this is correct or not, but have you tried long division?
  4. Apr 18, 2008 #3
    You should rewrite your polynomial as sum of partial fractions, hope you know how to do that. You write
    [tex]f(x) = \frac{x^3 + 3x + 12} { x(x+2)^2} = \frac{A}{x}+\frac{B}{x+2}+\frac{C}{(x+2)^2} [/tex]

    Where A,B,C are constants. Then you have to solve a system of three equations for A,B,C. Else you look in math book or wikipedia under partial fractions.
  5. Apr 18, 2008 #4
    Thanks! It is about partial fractions.
  6. Apr 18, 2008 #5


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    Staff Emeritus
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    I would strongly recommend that you multiply out the denominator and divide first. "Partial fractions" only works correctly when the numerator is of lower degree than the denominator.
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