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Math Help - Help With This Partial Fraction Evaluation

  1. #1
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    Help With This Partial Fraction Evaluation

    I'm working on evaluating this integral using partial fractions:

    the indefinite integral of (-2x+4)/((x^2+1)(x-1)^2) and I've gotten it down to Ax+B/x^+1+C/x-1+D/(x-1)^2. Now how to I find what coefficients correspond with each term? I know what they are using a partial fraction tool online, but obviously I want to be able to do it and show I can do it on my own!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by fattydq View Post
    I'm working on evaluating this integral using partial fractions:

    the indefinite integral of (-2x+4)/((x^2+1)(x-1)^2) and I've gotten it down to Ax+B/x^+1+C/x-1+D/(x-1)^2. Now how to I find what coefficients correspond with each term? I know what they are using a partial fraction tool online, but obviously I want to be able to do it and show I can do it on my own!
    please use parentheses. you seem to have \frac {-2x + 1}{(x^2 + 1)(x - 1)^2} = \frac {Ax + B}{x^2 + 1} + \frac C{x - 1} + \frac D{(x - 1)^2}

    this is correct. next, multiply through by the denominator of the left hand side. you get

    -2x + 4 = (Ax + B)(x - 1)^2 + C(x^2 + 1)(x - 1) + D(x^2 + 1)

    plug in x = 1: 2 = 2D

    plug in x = 0: 4 = B - C + D

    plug in x = -1: 6 = 4(B - A) -4C + 2D

    plug in x = 2: 0 = 2A + B + 5C + 5D

    hence you have four equations with four unknowns. you can solve this system simultaneously.
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