- (a) Express \(\frac { 3 x } { ( 2 x - 1 ) ( x - 2 ) }\) in partial fraction form.
(b) Hence show that
$$\int _ { 5 } ^ { 25 } \frac { 3 x } { ( 2 x - 1 ) ( x - 2 ) } d x = \ln k$$
where \(k\) is a fully simplified fraction to be found.
(Solutions relying entirely on calculator technology are not acceptable.)