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

[Susie babe]

Homework Statement

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

Homework Equations

None

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.

 

[eumyang]

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.

 

[sandy.bridge]

The degree of the numerator is equal to the degree of the denominator. Try long division before partial fraction decomposition.

 

[Ray Vickson]

Homework Statement

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

Homework Equations

None

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
$$3x^2-10 = 3(x^2-4x+4)+12x - 22.$$

 

[Susie babe]

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.