Integration by partial fractions?

[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 got to do polynomial long division... I need a review of polynomial long division; Lol.

 

[Simon Bridge]

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 got to do polynomial long division... I need a review of polynomial long division; Lol.

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

 

[lurflurf]

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

 

[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?