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Thread: Nonrepeated Linear Factors

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    Nonrepeated Linear Factors

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

    $\displaystyle
    \int \frac{dx}{1-x^{2}}
    $
    Last edited by thatloserrsaid; Feb 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....

    $\displaystyle
    \int \frac{dx}{1-x^{2}}
    $
    $\displaystyle \frac{1}{(1-x)(1+x)} = \frac{A}{1-x} + \frac{B}{1+x}$

    $\displaystyle 1 = A(1+x) + B(1-x)$

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

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

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