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Math Help - please help me with integration using partial fraction method

  1. #1
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    please help me with integration using partial fraction method

    Can you help me with this..... using partial fraction method

    integration of:

    x^3 +4x^2 -6x / x^2 -2x+1



    I used polynomial division and obtained..

    (x+6) + (5x-6)/(x^2-2x +1)

    is this right?? and.. can you give me solution with explanation pls..

    Thank you so much
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  2. #2
    Senior Member MacstersUndead's Avatar
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    Your long division is correct.

    Now you can easily integrate (x+6) by itself.

    As for the remainder, consider that (a+b)/(c) = a/c + b/c
    and that x^2 - 2x + 1 = (x-1)^2
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  3. #3
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    \frac{5x-6}{(x-1)^2} = \frac{A}{x-1} + \frac{B}{(x-1)^2}

    5x-6 = A(x-1) + B

    let x = 1 ...

    -1 = B

    let x = 0 ...

    -6 = -A - 1

    A = 5

    \frac{5x-6}{(x-1)^2} = \frac{5}{x-1} - \frac{1}{(x-1)^2}<br />
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