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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 15x-14=(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, 14=2A+B. We can solve these to get A=-1, B=16. So, Combining all this, we get

-- MattGuay - 2009-10-07

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