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

  • Thread starter Hevonen
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  • #1
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Homework Statement



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

Homework Equations




The Attempt at a Solution



I know that i should somehow rewrite the polynomial but I do not know how. Please, help me.
 

Answers and Replies

  • #2
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Hmm, I don't know if this is correct or not, but have you tried long division?
 
  • #3
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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.
 
  • #4
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Thanks! It is about partial fractions.
 
  • #5
HallsofIvy
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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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