Express \(\frac { 3 + 13 x - 6 x ^ { 2 } } { 2 x - 3 }\) in the form \(A x + B + \frac { C } { 2 x - 3 }\).
Show that \(\int _ { 3 } ^ { 6 } \frac { 3 + 13 x - 6 x ^ { 2 } } { 2 x - 3 } \mathrm {~d} x = p + q \ln 3\), where \(p\) and \(q\) are rational numbers. [0pt]
[4 marks]