Can you help me with this..... using partial fraction method

integration of:

x^3 +4x^2 -6x / x^2 -2x+1

I used polynomial division and obtained..

(x+6) + (5x-6)/(x^2-2x +1)

is this right?? and.. can you give me solution with explanation pls..

Thank you so much

2. Your long division is correct.

Now you can easily integrate (x+6) by itself.

As for the remainder, consider that (a+b)/(c) = a/c + b/c
and that x^2 - 2x + 1 = (x-1)^2

3. $\frac{5x-6}{(x-1)^2} = \frac{A}{x-1} + \frac{B}{(x-1)^2}$

$5x-6 = A(x-1) + B$

let $x = 1$ ...

$-1 = B$

let $x = 0$ ...

$-6 = -A - 1$

$A = 5$

$\frac{5x-6}{(x-1)^2} = \frac{5}{x-1} - \frac{1}{(x-1)^2}
$