Evaluate the integral (x - 1) / (x^2 - 2x + 5) dx

Can you please show your steps?
Thank you

(x - 1) / (x^2 - 2x + 5) dx
u = x²-2x+5 → du = (2x-2) dx
du = 2(x-1) dx
(x-1)dx = ½ du

= ½ ∫ u^-1 du
= ½ ln u + c
= ½ ln(x² - 2x + 5) + c

Hint:
u = (x^2 - 2x + 5)