3. Given that
$$4 x ^ { 3 } + 2 x ^ { 2 } + 17 x + 8 \equiv ( A x + B ) \left( x ^ { 2 } + 4 \right) + C x + D$$
- find the values of the constants \(A , B , C\) and \(D\).
- Hence find
$$\int _ { 1 } ^ { 4 } \frac { 4 x ^ { 3 } + 2 x ^ { 2 } + 17 x + 8 } { x ^ { 2 } + 4 } d x$$
giving your answer in the form \(p + \ln q\), where \(p\) and \(q\) are integers.