Evaluate: ∫ (3x+5)/(x³ - x² - x + 1) dx

$x^3 - x^2 - x + 1 = (x-1)^2(x+1)$. $\frac{3x+5}{(x-1)^2(x+1)} = \frac{A}{x-1} + \frac{B}{(x-1)^2} + \frac{C}{x+1}$. Putting $x=1$: $B = \frac{8}{2} = 4$. Putting $x=-1$: $C = \frac{2}{4} = \frac{1}{2}$. Comparing $x^2$: $A + C = 0$, so $A = -\frac{1}{2}$. $\int = -\frac{1}{2}\log|x-1| + 4\int(x-1)^{-2}dx + \frac{1}{2}\log|x+1|$. Hence the integral is $-\frac{1}{2}\log|x-1| - \frac{4}{x-1} + \frac{1}{2}\log|x+1| + C$.