4 It is given that, for \(n \geqslant 0 , \mathrm { I } _ { \mathrm { n } } = \int _ { 0 } ^ { \ln 3 } \operatorname { sech } ^ { \mathrm { n } } \mathrm { xdx }\).
- Show that, for \(n \geqslant 2\),
$$( n - 1 ) \mathrm { I } _ { n } = \left( \frac { 3 } { 5 } \right) ^ { n - 2 } \left( \frac { 4 } { 5 } \right) + ( n - 2 ) \mathrm { I } _ { n - 2 }$$
[You may use the result that \(\frac { \mathrm { d } } { \mathrm { dx } } ( \operatorname { sech } x ) = - \tanh x \operatorname { sech } x\).]
- Find the value of \(I _ { 4 }\).