# Nonrepeated Linear Factors

• Feb 24th 2010, 02:18 PM
thatloserrsaid
Nonrepeated Linear Factors
I need to express the integrand as a sum of partial fractions and evaluate the integral....

$
\int \frac{dx}{1-x^{2}}
$
• Feb 24th 2010, 03:24 PM
skeeter
Quote:

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

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

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

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

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

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

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