Given that \(y = 2 x ^ { 2 } - 8 x + 3\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
Hence, or otherwise, find
$$\int _ { 4 } ^ { 6 } \frac { x - 2 } { 2 x ^ { 2 } - 8 x + 3 } d x$$
giving your answer in the form \(k \ln 3\), where \(k\) is a rational number.
Use the substitution \(u = 3 x - 1\) to find \(\int x \sqrt { 3 x - 1 } \mathrm {~d} x\), giving your answer in terms of \(x\).