- Given that
$$\frac { 3 x + 4 } { ( x - 2 ) ( 2 x + 1 ) ^ { 2 } } \equiv \frac { A } { x - 2 } + \frac { B } { 2 x + 1 } + \frac { C } { ( 2 x + 1 ) ^ { 2 } }$$
- find the values of the constants \(A , B\) and \(C\).
- Hence find the exact value of
$$\int _ { 7 } ^ { 12 } \frac { 3 x + 4 } { ( x - 2 ) ( 2 x + 1 ) ^ { 2 } } \mathrm {~d} x$$
giving your answer in the form \(p \ln q + r\) where \(p\), \(q\) and \(r\) are rational numbers.