Integration by partial fractions?


by James2
Tags: factoring, integral, integration, polynomial, rational
James2
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Nov14-12, 09:03 PM
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Whoa, this here is kicking me hard! Okay, so I've got everything pretty well down until... stuff like... [tex]\int \frac{3x + 32}{x^{2}-16x + 64}dx[/tex]

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.
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Simon Bridge
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Nov15-12, 02:22 AM
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Quote Quote by James2 View Post
Whoa, this here is kicking me hard! Okay, so I've got everything pretty well down until... stuff like... [tex]\int \frac{3x + 32}{x^{2}-16x + 64}dx[/tex]

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.
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/C...rtialFrac.html
lurflurf
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Nov15-12, 05:26 AM
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x^2-16x+64=(x-8)^2
3x+32=3(x-8)+56

Simon Bridge
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Nov15-12, 05:31 PM
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Integration by partial fractions?


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


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