- Given that
$$( x - 5 ) ( 2 x + 1 ) ( x + 3 ) \equiv a x ^ { 3 } + b x ^ { 2 } - 32 x - 15$$
where \(a\) and \(b\) are constants,
- find the value of \(a\) and the value of \(b\).
- Hence find
$$\int \frac { ( x - 5 ) ( 2 x + 1 ) ( x + 3 ) } { 5 \sqrt { x } } \mathrm {~d} x$$
writing each term in simplest form.