Find the quotient and remainder when \(2 x ^ { 3 } + x ^ { 2 } - 8 x\) is divided by ( \(2 x + 1\) ).
Hence find the exact value of \(\int _ { 0 } ^ { 3 } \frac { 2 x ^ { 3 } + x ^ { 2 } - 8 x } { 2 x + 1 } \mathrm {~d} x\), giving the answer in the form \(\ln \left( k \mathrm { e } ^ { a } \right)\) where \(k\) and \(a\) are constants.