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

[Hevonen]

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.

 

[amolv06]

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

 

[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.

 

[Hevonen]

Thanks! It is about partial fractions.

 

[HallsofIvy]

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.