6. Given that \(\mathrm { f } ( x ) = \left( 2 x ^ { \frac { 3 } { 2 } } - 3 x ^ { - \frac { 3 } { 2 } } \right) ^ { 2 } + 5 , x > 0\),
- find, to 3 significant figures, the value of \(x\) for which \(\mathrm { f } ( x ) = 5\).
- Show that \(\mathrm { f } ( x )\) may be written in the form \(A x ^ { 3 } + \frac { B } { x ^ { 3 } } + C\), where \(A , B\) and \(C\) are constants to be found.
- Hence evaluate \(\int _ { 1 } ^ { 2 } f ( x ) d x\).