- (a) Given that \(k\) is a constant, find
$$\int \left( \frac { 4 } { x ^ { 3 } } + k x \right) \mathrm { d } x$$
simplifying your answer.
(b) Hence find the value of \(k\) such that
$$\int _ { 0.5 } ^ { 2 } \left( \frac { 4 } { x ^ { 3 } } + k x \right) \mathrm { d } x = 8$$