(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the exact values of A, B, and C in the following partial fraction decomposition.Then obtain the integral using those values.

1/(x^3-3x^2) = A/x + B/x^2 + C/(x-3)

2. Relevant equations

I'm not sure at this point.

3. The attempt at a solution

To make the denominator on the right equal to the left...

A(x^2)(x-3) + B(x)(x-3) + C(x)(x^2)

so.....

1 = Ax^3 +Cx^3 -3Ax^2 +Bx^2 -3Bx

From cubic values..

A + C = 0 So A= -C

From squared values...

-3A + B = 0 So A = 1/3B which also means C = -1/3B

From x values..

-3B = 0.

Here is where im at a loss. The x value equation cannot possibly be correct. It would denote that B=0, therefore A and C also equal 0. Am I doing something incorrectly in my multiplication? If not, how is it possible to use the partial fractional decomposition method to make an equation for integration?

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# Partial Fractional Decomposition to obtain an integral.

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