# Thread: Help With This Partial Fraction Evaluation

1. ## Help With This Partial Fraction Evaluation

I'm working on evaluating this integral using partial fractions:

the indefinite integral of (-2x+4)/((x^2+1)(x-1)^2) and I've gotten it down to Ax+B/x^+1+C/x-1+D/(x-1)^2. Now how to I find what coefficients correspond with each term? I know what they are using a partial fraction tool online, but obviously I want to be able to do it and show I can do it on my own!

2. Originally Posted by fattydq
I'm working on evaluating this integral using partial fractions:

the indefinite integral of (-2x+4)/((x^2+1)(x-1)^2) and I've gotten it down to Ax+B/x^+1+C/x-1+D/(x-1)^2. Now how to I find what coefficients correspond with each term? I know what they are using a partial fraction tool online, but obviously I want to be able to do it and show I can do it on my own!
please use parentheses. you seem to have $\displaystyle \frac {-2x + 1}{(x^2 + 1)(x - 1)^2} = \frac {Ax + B}{x^2 + 1} + \frac C{x - 1} + \frac D{(x - 1)^2}$

this is correct. next, multiply through by the denominator of the left hand side. you get

$\displaystyle -2x + 4 = (Ax + B)(x - 1)^2 + C(x^2 + 1)(x - 1) + D(x^2 + 1)$

plug in $\displaystyle x = 1$: $\displaystyle 2 = 2D$

plug in $\displaystyle x = 0$: $\displaystyle 4 = B - C + D$

plug in $\displaystyle x = -1$: $\displaystyle 6 = 4(B - A) -4C + 2D$

plug in $\displaystyle x = 2$: $\displaystyle 0 = 2A + B + 5C + 5D$

hence you have four equations with four unknowns. you can solve this system simultaneously.