5 The polynomial \(\mathrm { p } ( x )\) is defined by \(\mathrm { p } ( x ) = 9 x ^ { 3 } + 18 x ^ { 2 } + 5 x + 4\).
- Find the quotient when \(\mathrm { p } ( x )\) is divided by \(( 3 x + 2 )\), and show that the remainder is 6 .
\includegraphics[max width=\textwidth, alt={}, center]{76df3465-9617-4f2b-a8b7-f474b2817504-08_2713_33_146_2012}
\includegraphics[max width=\textwidth, alt={}, center]{76df3465-9617-4f2b-a8b7-f474b2817504-09_2723_33_138_20} - Find the value of \(\int _ { 0 } ^ { 2 } \frac { \mathrm { p } ( x ) } { 3 x + 2 } \mathrm {~d} x\) ,giving your answer in the form \(a + \ln b\) where \(a\) and \(b\) are integers.