# Thread: Integrating by partial fractions

1. ## Integrating by partial fractions

I need to use partial fractions to derive the integration formula

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

So far I've broken the equation into

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

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

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.

I need to use partial fractions to derive the integration formula

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

So far I've broken the equation into

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

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

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.
let $\displaystyle x = a$ , solve for B
then let $\displaystyle x = -a$ , solve for A