Quick question with the antederivative

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SUMMARY

The discussion focuses on finding the antiderivative of the function (x^3 + 3x^2)/(x^2 + 4x + 4). The recommended approach involves first dividing the polynomial to express it as a sum of a polynomial and a linear term over (x^2 + 4x + 4), which simplifies to (x + 2)^2. This allows for straightforward integration of the polynomial part, while the linear term can be integrated using partial fractions, although the latter may not be necessary for simpler cases.

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ddr
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hi!
who help me to find the antiderivative of:

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

thanks
 
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ddr said:
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!)
 
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