Partial fractions

1. Mar 11, 2012

schapman22

1. The problem statement, all variables and given/known data

We were given a worksheet to integrate some problems using partial fractions. This one however I cannot figure out what to do with it. This is the problem.

∫(x3-4x2+x+6)/(x2-x+2) dx

3. The attempt at a solution

using long division i got ∫(x-3) (-4(x-3)/(x2-x+2) dx
split it up into ∫xdx - 3∫dx - 4∫(x-3)/(x2-x+2)
now I don't know what to do with the x2-x+2?
any suggestions on how to proceed from here? Thanks in advance!

2. Mar 11, 2012

SammyS

Staff Emeritus
What you have done so far looks correct.

For the integral $\displaystyle \int 2\frac{2x-6}{x^2-x+2}\,dx\,,$ notice that the derivative of the denominator is 2x-1.

Split the integrand up into $\displaystyle 2\frac{2x-1}{x^2-x+2}+2\frac{-5}{x^2-x+2}\,.$

So you get two integrals. The first results in a logarithm. For the second one, complete the square in the denominator.

3. Mar 11, 2012

schapman22

So I'm allowed to multiple the integrand by 2?

4. Mar 11, 2012

thank you