5 It is given that, for non-negative integers \(n\),
$$I _ { n } = \int _ { 1 } ^ { \mathrm { e } } ( \ln x ) ^ { n } \mathrm {~d} x$$
- Show that, for \(n \geqslant 1\),
$$I _ { n } = \mathrm { e } - n I _ { n - 1 } .$$
- Find \(I _ { 3 }\) in terms of e.