(i)[5]
Determine the constants $A$, $B$, $C$ and $D$ so that $\frac{2x^3 - 1}{x^2(2x - 1)} \equiv A + \frac{B}{x} + \frac{C}{x^2} + \frac{D}{2x - 1}$.
(ii)[5]
Hence show that $\int_1^2 \frac{2x^3 - 1}{x^2(2x - 1)} \, dx = \frac{3}{2} + \frac{1}{2} \ln\left(\frac{16}{27}\right)$.