- (i) Find \(\frac { \mathrm { d } } { \mathrm { d } x } \ln \left( \sin ^ { 2 } 3 x \right)\) writing your answer in simplest form.
(ii) (a) Find \(\frac { \mathrm { d } } { \mathrm { d } x } \left( 3 x ^ { 2 } - 4 \right) ^ { 6 }\)
(b) Hence show that
$$\int _ { 0 } ^ { \sqrt { 2 } } x \left( 3 x ^ { 2 } - 4 \right) ^ { 5 } \mathrm {~d} x = R$$
where \(R\) is an integer to be found.
(Solutions relying on calculator technology are not acceptable.)