Problem

(a) Express

$$\frac{3x}{(2x-1)(x-2)}$$

in partial fraction form.

(b) Hence show that

$$\int_5^{25}\frac{3x}{(2x-1)(x-2)}\,dx=\ln k$$

where $k$ is a fully simplified fraction to be found.

(Solutions relying entirely on calculator technology are not acceptable.)