# Homework Help: Integration by partial fractions?

1. Nov 14, 2012

### James2

Whoa, this here is kicking me hard! Okay, so I've got everything pretty well down until... stuff like... $$\int \frac{3x + 32}{x^{2}-16x + 64}dx$$

So, I get how to factor the denominator, but then what? The above won't factor... Also, I read that if the degree of the numerator is higher than the denominator I gotta do polynomial long division... I need a review of polynomial long division; Lol.

Last edited by a moderator: Nov 15, 2012
2. Nov 15, 2012

### Simon Bridge

But the numerator is not higher order than the denominator and:$$\frac{3x + 32}{x^{2}-16x + 64}=\frac{3x+32}{(x-8)^2}$$See also:
http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/partialfracdirectory/PartialFrac.html

3. Nov 15, 2012

### lurflurf

x^2-16x+64=(x-8)^2
3x+32=3(x-8)+56

4. Nov 15, 2012

### Simon Bridge

... oh yes, and complete the square in the numerator.
Thanks lurflurf. The example does not seem to illustrate the following comments does it?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook