How to solve this partial fractions problem

integral of (x^3)/(x^2-2x+1) dx

First divide the numerator by the denominator to get x + 2 + (3x - 2)/(x^2 - 2x + 1)

Then factor the denominator to (x - 1)^2

(3x - 2)/(x - 1)^2 = A/(x - 1) + B/(x - 1)^2

Multiply by LCD of (x - 1)^2

3x - 2 = A(x - 1) + B

Equate the powers: 3 = A
-2 = -A + B --> -2 = -3 + B --> B = 1

The integrand will now be x + 2 + 3/(x - 1) + 1/(x - 1)^2

Then integrate