9 Let \(\mathrm { f } ( x ) = \frac { 2 x ^ { 2 } + 17 x - 17 } { ( 1 + 2 x ) ( 2 - x ) ^ { 2 } }\).
- Express \(\mathrm { f } ( x )\) in partial fractions.
- Hence show that \(\int _ { 0 } ^ { 1 } \mathrm { f } ( x ) \mathrm { d } x = \frac { 5 } { 2 } - \ln 72\).
\includegraphics[max width=\textwidth, alt={}, center]{60bb482b-fa41-42ea-a112-62851e5a19aa-16_524_725_269_696}
The diagram shows the curve \(y = ( x + 5 ) \sqrt { 3 - 2 x }\) and its maximum point \(M\).