- (a) Given that
$$\frac { x ^ { 2 } + 8 x - 3 } { x + 2 } \equiv A x + B + \frac { C } { x + 2 } \quad x \in \mathbb { R } \quad x \neq - 2$$
find the values of the constants \(A , B\) and \(C\)
(b) Hence, using algebraic integration, find the exact value of
$$\int _ { 0 } ^ { 6 } \frac { x ^ { 2 } + 8 x - 3 } { x + 2 } d x$$
giving your answer in the form \(a + b \ln 2\) where \(a\) and \(b\) are integers to be found.