# Integrals using long division

1. Feb 25, 2013

### Cacophony

1. The problem statement, all variables and given/known data
∫(2x+1)/(x²+2x+1)(x²+x+1)

2. Relevant equations
none

3. The attempt at a solution
I've foiled this out to look like:

∫(2x+1)/(x^4+3x³+4x²+3x+1)

I'm trying long division here but it's getting really ugly really fast. Should I foil this out in the first place or should I use a different approach?

2. Feb 25, 2013

### SteamKing

Staff Emeritus
I would try a different approach.

Look at the denominator and see if it can be factored rather than multiplied together.

3. Feb 25, 2013

### eumyang

Why would you try long division? You are dividing something "smaller" into something "bigger". It is as if you are suggesting that to evaluate $\frac{7}{584}$ you divide 584 by 7.

Have you considered using partial fractions to split the integral into two?

4. Feb 25, 2013

### iRaid

Definitely do partial fractions. The only time you do long division is when the degree on top is bigger than the bottom.

5. Feb 25, 2013

### Staff: Mentor

Or when the degrees are equal.