- (i) Find
$$\int x ^ { 2 } \mathrm { e } ^ { x } \mathrm {~d} x$$
(4)
(ii) Use the substitution \(u = \sqrt { 1 - 3 x }\) to show that
$$\int \frac { 27 x } { \sqrt { 1 - 3 x } } \mathrm {~d} x = - 2 ( 1 - 3 x ) ^ { \frac { 1 } { 2 } } ( A x + B ) + k$$
where \(A\) and \(B\) are integers to be found and \(k\) is an arbitrary constant.