Quick question with the antederivative

[ddr]

hi!
who help me to find the antiderivative of:

(x^3 + 3x^2)/(x^2 + 4x + 4)

thanks

 

[HallsofIvy]

hi!
who help me to find the antiderivative of:

(x^3 + 3x^2)/(x^2 + 4x + 4)

thanks

You sure this is not homework?

First divide so that you have p(x)+ (Ax+ B)/x^2+ 4x+ 4): a polynomial plus a linear term over x^2+ 4x+ 4. You should be able to integrate the polynomial easily. Now use the fact that x^2+ 4x+ 4= (x+2)^2 and partial fractions.
(I just did the division myself: Ax+ B is simple enough that you don't need partial fractions!)