(x² - 2x + 2)' = 2x - 2,2x - 3 = (2x - 2) - 1
∫ (2x - 3)/(x² - 2x + 2) dx
= ∫ [(2x - 2) - 1]/(x² - 2x + 2) dx
= ∫ (2x - 2)/(x² - 2x + 2) dx - ∫ dx/(x² - 2x + 2)
= ∫ d(x² - 2x + 2)/(x² - 2x + 2) - ∫ d(x - 1)/[(x - 1)² + 1],【∫ dx/(x² + a²) = (1/a)arctan(x/a) + C】
= ln[(x - 1)² + 1] - arctan(x - 1) + C