Show that the substitution \(u = \sqrt { x }\) transforms \(\int \frac { 1 } { x ( 1 + \sqrt { x } ) } \mathrm { d } x\) to \(\int \frac { 2 } { u ( 1 + u ) } \mathrm { d } u\).
Hence find the exact value of \(\int _ { 1 } ^ { 9 } \frac { 1 } { x ( 1 + \sqrt { x } ) } \mathrm { d } x\).