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Math Help - Partial Fraction Integrals

  1. #1
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    Partial Fraction Integrals

    Hey i've got 3 integrals i need to solve which are the following.

    \int \frac{x^2-2}{(x+1)(x-2)}
    \int \frac{x-1}{(x+1)(x-2)^2}
    \int \frac{1}{(x+1)(x^2+2x+2)}

    For every other example i've done, before I convert the fraction to something I can integrate the question tells me what form to put the equation in.

    So my question is how do i know what form do i have to put the fraction in before i integrate i.e.


    \int \frac{x^2-2}{(x+1)(x-2)} = \int \frac{A}{x+1} +\int \frac{Bx+C}{x-2}

    or would it be something like

    \int \frac{x^2-2}{(x+1)(x-2)} = \int A + \int \frac{Bx+C}{x+1} + \int\frac{D}{x-2}
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by Kevlar View Post
    Hey i've got 3 integrals i need to solve which are the following.

    \int \frac{x^2-2}{(x+1)(x-2)}
    \int \frac{x-1}{(x+1)(x-2)^2}
    \int \frac{1}{(x+1)(x^2+2x+2)}

    For every other example i've done, before I convert the fraction to something I can integrate the question tells me what form to put the equation in.

    So my question is how do i know what form do i have to put the fraction in before i integrate i.e.


    \int \frac{x^2-2}{(x+1)(x-2)} = \int \frac{A}{x+1} +\int \frac{Bx+C}{x-2}

    or would it be something like

    \int \frac{x^2-2}{(x+1)(x-2)} = \int A + \int \frac{Bx+C}{x+1} + \int\frac{D}{x-2}

    \int \frac{x^2-2}{(x+1)(x-2)} dx

    \int \frac{x^2-4 +2 }{(x+1)(x-2)} dx

    \int \frac{(x-2)(x+2)}{(x+1)(x-2)} dx + \int \frac{2}{(x+1)(x-2)} dx

    \int \frac{(x+1)}{(x+1)} + \frac{1}{(x+1)} dx + \int \frac{2}{(x+1)(x-2)} dx

    \frac{2}{(x+1)(x-2)} = \frac{A}{x+1} + \frac{B}{x-2}

    find A and B I think A=-2/3 and B=2/3
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