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

by Susie babe
Tags: calculus 2, integral
 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.
HW Helper
P: 1,347
 Quote by Susie babe 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...
$$\frac{A}{x - 2} + \frac{B}{(x - 2)^2}$$
... 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.
 P: 778 The degree of the numerator is equal to the degree of the denominator. Try long division before partial fraction decomposition.
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Thanks
P: 5,086
Indefinite Integral of (3x^2-10)/(x^2-4x+4) dx using PARTIAL FRACTION

 Quote by Susie babe 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
$$3x^2-10 = 3(x^2-4x+4)+12x - 22.$$
 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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