# Thread: Partial Fraction Decomp Integral

1. ## Partial Fraction Decomp Integral

$\displaystyle \int \frac{6x^2 - 10x + 1}{(x-2)(x-1)^2} dx$
Can someone explain the partial fraction decomposition part of this problem. I'll be able to take the integrating from there, just need help in understanding this concept.
I know you write it as $\displaystyle \frac{A}{x-2} + \frac{B}{x-1} + \frac{C}{(x-1)^2}$
If someone could explain how to go about doing the next parts that would be great.

2. Originally Posted by VitaX
$\displaystyle \int \frac{6x^2 - 10x + 1}{(x-2)(x-1)^2} dx$
Can someone explain the partial fraction decomposition part of this problem. I'll be able to take the integrating from there, just need help in understanding this concept.
I know you write it as $\displaystyle \frac{A}{x-2} + \frac{B}{x-1} + \frac{C}{(x-1)^2}$
If someone could explain how to go about doing the next parts that would be great.
Solve for $\displaystyle A,B,C$ for $\displaystyle 6x^2 - 10x + 1 = A(x-1)^2+B(x-1)(x-2)+C(x-2)$

Now see what happens when you sub $\displaystyle x=1,-2$