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

$\displaystyle

\int \frac{dx}{1-x^{2}}

$

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- Feb 24th 2010, 01:18 PMthatloserrsaidNonrepeated 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}}

$ - Feb 24th 2010, 02:24 PMskeeter
$\displaystyle \frac{1}{(1-x)(1+x)} = \frac{A}{1-x} + \frac{B}{1+x}$

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

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

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

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