2.
$$g ( x ) = \frac { 2 x ^ { 2 } - 5 x + 8 } { x - 2 }$$
- Write \(g ( x )\) in the form
$$A x + B + \frac { C } { x - 2 }$$
where \(A , B\) and \(C\) are integers to be found.
- Hence use algebraic integration to show that
$$\int _ { 4 } ^ { 8 } \mathrm {~g} ( x ) \mathrm { d } x = \alpha + \beta \ln 3$$
where \(\alpha\) and \(\beta\) are integers to be found.