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Indefinite Integral of (3x^2-10)/(x^2-4x+4) dx using PARTIAL FRACTION

by Susie babe
Tags: calculus 2, integral
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Susie babe
#1
Feb27-13, 04:29 PM
P: 3
1. The problem statement, all variables and given/known data

Integrate (3x^2-10)/(x^2-4x+4) dx using partial fractions.


2. Relevant equations

None

3. The attempt at a solution

I tried using A/(x-2) + B/(x-2)^2 but I didnt get a coeffecient of an x^2.

I've also tried using (Ax+B)/(x-2) + C/(x-2)^2



Though I honestly thought that the usual A/(x-2) + B/(x-2)^2 would work, How do I know which formula to use. I know you have to do long division if the numerator has an x to a larger value than that of the denominator. I know when you have something like: (x^2-1) or (x^3+2) in the denominator then you use the Ax+B, Cx+D formula.
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eumyang
#2
Feb27-13, 04:33 PM
HW Helper
P: 1,347
Quote Quote by Susie babe View Post
3. The attempt at a solution

I tried using A/(x-2) + B/(x-2)^2 but I didnt get a coeffecient of an x^2.

I've also tried using (Ax+B)/(x-2) + C/(x-2)^2



Though I honestly thought that the usual A/(x-2) + B/(x-2)^2 would work, How do I know which formula to use.
The last thing that you said is correct...
[tex]\frac{A}{x - 2} + \frac{B}{(x - 2)^2}[/tex]
... because the denominator is a linear factor squared. But before you try partial fractions, you have to use long division because the degrees of the numerator and denominator are the same.
sandy.bridge
#3
Feb27-13, 04:34 PM
P: 778
The degree of the numerator is equal to the degree of the denominator. Try long division before partial fraction decomposition.

Ray Vickson
#4
Feb27-13, 05:02 PM
Sci Advisor
HW Helper
Thanks
P: 5,086
Indefinite Integral of (3x^2-10)/(x^2-4x+4) dx using PARTIAL FRACTION

Quote Quote by Susie babe View Post
1. The problem statement, all variables and given/known data

Integrate (3x^2-10)/(x^2-4x+4) dx using partial fractions.


2. Relevant equations

None

3. The attempt at a solution

I tried using A/(x-2) + B/(x-2)^2 but I didnt get a coeffecient of an x^2.

I've also tried using (Ax+B)/(x-2) + C/(x-2)^2



Though I honestly thought that the usual A/(x-2) + B/(x-2)^2 would work, How do I know which formula to use. I know you have to do long division if the numerator has an x to a larger value than that of the denominator. I know when you have something like: (x^2-1) or (x^3+2) in the denominator then you use the Ax+B, Cx+D formula.
Re-write the numerator as
[tex] 3x^2-10 = 3(x^2-4x+4)+12x - 22.[/tex]
Susie babe
#5
Feb27-13, 07:52 PM
P: 3
Ah, so if the degree of the numerator and that of the denominator are the same then you have to use long division, didnt know that. Thanks a lot guys it worked out well.


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