Solving Partial Fractions with Polynomial Division

[beaf123]

Homework Statement

∫ (x^3)/(x^2+2x+1)

I think I could solve it if I knew how they did this operation:

From the solution:
'
(x^3)/(x^2+2x+1) = (x-2) + (3x+2)/(x+1)^2 ( After long division)

Did they use polynomialdivision?

x^3: x^2-2X+1=

If so, how?

 

[Mentallic]

Yes, long division was used. Do you know how to use it?

This video will help http://www.youtube.com/watch?v=ok4k6HDCuIk and just keep in mind that when applying it to your problem,

$$x^3=1x^3+0x^2+0x+0$$

 

[SammyS]

Homework Statement

∫ (x^3)/(x^2+2x+1) dx

I think I could solve it if I knew how they did this operation:

From the solution:
'
(x^3)/(x^2+2x+1) = (x-2) + (3x+2)/(x+1)^2 ( After long division)

Did they use polynomial division?

x^3: x^2-2X+1=

If so, how?

Yes, they used long division for polynomials.

Here's a link to Wikipedia's page on polynomial long division.

If you don't want to use long division, use the substitution u = x+1.