6 Let \(I _ { n } = \int _ { 0 } ^ { 1 } x ^ { n } ( 1 - x ) ^ { \frac { 1 } { 2 } } \mathrm {~d} x\), for \(n \geqslant 0\). Show that, for \(n \geqslant 1\),
$$( 3 + 2 n ) I _ { n } = 2 n I _ { n - 1 }$$
Hence find the exact value of \(I _ { 3 }\).