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 .
- Find the value of \(\int _ { 0 } ^ { 2 } \frac { \mathrm { p } ( x ) } { 3 x + 2 } \mathrm {~d} x\), giving your answer in the form \(\mathrm { a } + \operatorname { lnb }\) where \(a\) and \(b\) are integers.
\includegraphics[max width=\textwidth, alt={}, center]{6ee58f43-831d-402c-9f9a-2b247b2f7ffc-10_414_693_276_687}
The diagram shows the curve with equation \(\mathrm { y } = \frac { \ln ( 2 \mathrm { x } + 1 ) } { \mathrm { x } + 3 }\). The curve has a maximum point \(M\).