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

1. Homework Statement

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

2. Homework 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.

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

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.

Thanks! It is about partial fractions.

HallsofIvy