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Math Help - Integrating by partial fractions

  1. #1
    Newbie madmartigano's Avatar
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    Integrating by partial fractions

    I need to use partial fractions to derive the integration formula

    \int {\frac{{dx}}{{{a^2} - {x^2}}}}  = \frac{1}{{2a}}\ln \left| {\frac{{a + x}}{{a - x}}} \right| + C

    So far I've broken the equation into

    \frac{1}{{{a^2} - {x^2}}} = \frac{A}{{a + x}} + \frac{B}{{a - x}}

      1 = A(a - x) + B(a + x)

    I'm trying to determine the coefficients of A and B, but I can't figure out how to proceed with the derivation from here.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by madmartigano View Post
    I need to use partial fractions to derive the integration formula

    \int {\frac{{dx}}{{{a^2} - {x^2}}}}  = \frac{1}{{2a}}\ln \left| {\frac{{a + x}}{{a - x}}} \right| + C

    So far I've broken the equation into

    \frac{1}{{{a^2} - {x^2}}} = \frac{A}{{a + x}} + \frac{B}{{a - x}}

      1 = A(a - x) + B(a + x)

    I'm trying to determine the coefficients of A and B, but I can't figure out how to proceed with the derivation from here.
    using your last equation ...

    let x = a , solve for B

    then let x = -a , solve for A
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