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Math Help - Nonrepeated Linear Factors

  1. #1
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    Nonrepeated Linear Factors

    I need to express the integrand as a sum of partial fractions and evaluate the integral....

    <br />
\int \frac{dx}{1-x^{2}}<br />
    Last edited by thatloserrsaid; February 24th 2010 at 01:32 PM.
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  2. #2
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    Quote Originally Posted by thatloserrsaid View Post
    I need to express the integrand as a sum of partial fractions and evaluate the integral....

    <br />
\int \frac{dx}{1-x^{2}}<br />
    \frac{1}{(1-x)(1+x)} = \frac{A}{1-x} + \frac{B}{1+x}

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

    let x = 1 ... A = \frac{1}{2}

    let x = -1 ... B = \frac{1}{2}

    \frac{1}{(1-x)(1+x)} = \frac{1}{2}\left(\frac{1}{1-x} + \frac{1}{1+x}\right)
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