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# Integral of X^4/((X-1) * (X-2))

I'm doing this for homework and I can't figure out how to simplify X^4/((X-1) * (X-2)). Please help.

-- Main.jts228 - 2009-10-07

(x-1)*(x-2) = x^2-3x+2. So, we can do polynomial long division to get: Then, we can do partial fraction decomposition on to find an equivalent expression of the form Clearing denominators gives us the equation
15x-14=A(x-2)+B(x-1), which we can rearrange as
=(A+B)x-(2A+B).
Then, equate the x coefficients on both sides, and the constant expressions on both sides to get the system of equations A+B=15,
2A+B=14.
We can solve these to get A=-1, B=16. So, Combining all this, we get .
Which can be integrated term-by-term.

-- MattGuay - 2009-10-07

...and for the details of the partial fractions decomposition: in the initial box with the short answer, each of these links invites you to Show steps which reveals possible steps to arrive at the solution. The entire partial fractions decomposition in the first link is implicit in the long division of its first step.

-- DickFurnas - 2010-01-26

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Title Integral of X^4/((X-1) * (X-2))
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I Attachment History Action Size Date Who Comment png integral.png r1 manage 28.3 K 2010-01-26 - 18:47 DickFurnas integral result png partialfractions.png r1 manage 28.0 K 2010-01-26 - 18:47 DickFurnas partial fraction result
Topic revision: r5 - 2010-01-26 - DickFurnas    Copyright © by the contributing authors. All material on this collaboration platform is the property of the contributing authors.