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

1. Apr 18, 2008

Hevonen

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. Apr 18, 2008

amolv06

Hmm, I don't know if this is correct or not, but have you tried long division?

3. Apr 18, 2008

fikus

You should rewrite your polynomial as sum of partial fractions, hope you know how to do that. You write
$$f(x) = \frac{x^3 + 3x + 12} { x(x+2)^2} = \frac{A}{x}+\frac{B}{x+2}+\frac{C}{(x+2)^2}$$

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. Apr 18, 2008

Hevonen

Thanks! It is about partial fractions.

5. Apr 18, 2008

HallsofIvy

Staff Emeritus
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.