Use integration by parts to find \(\int x \mathrm { e } ^ { 5 x } \mathrm {~d} x\).
Use the substitution \(u = \sqrt { x }\) to show that
$$\int \frac { 1 } { \sqrt { x } ( 1 + \sqrt { x } ) } \mathrm { d } x = \int \frac { 2 } { 1 + u } \mathrm {~d} u$$
Find the exact value of \(\int _ { 1 } ^ { 9 } \frac { 1 } { \sqrt { x } ( 1 + \sqrt { x } ) } \mathrm { d } x\).