- In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
$$f ( x ) = \frac { 2 x ^ { 3 } - 4 x - 15 } { x ^ { 2 } + 3 x + 4 }$$
- Show that
$$f ( x ) \equiv A x + B + \frac { C ( 2 x + 3 ) } { x ^ { 2 } + 3 x + 4 }$$
where \(A , B\) and \(C\) are integers to be found.
- Hence, find
$$\int _ { 3 } ^ { 5 } \mathrm { f } ( x ) \mathrm { d } x$$
giving your answer in the form \(p + \ln q\), where \(p\) and \(q\) are integers.