4. (i) Find, without using a calculator,
$$\int _ { 3 } ^ { 5 } \frac { 1 } { \sqrt { 15 + 2 x - x ^ { 2 } } } d x$$
giving your answer as a multiple of \(\pi\).
(ii)
- Show that
$$5 \cosh x - 4 \sinh x = \frac { \mathrm { e } ^ { 2 x } + 9 } { 2 \mathrm { e } ^ { x } }$$
- Hence, using the substitution \(u = e ^ { x }\) or otherwise, find
$$\int \frac { 1 } { 5 \cosh x - 4 \sinh x } d x$$