0606 P12 - Jun 2022 - Q7 - 8 marks
7797
(a) Show that
\(\frac{2}{2x+3}-\frac{1}{x-1}+\frac{1}{(x-1)^2}\)
can be written as
\(\frac{8-3x}{(x-1)^2(2x+3)}.\)
(b) Find
\(\int_2^a \frac{8-3x}{(x-1)^2(2x+3)}\,dx,\)
where \(a\gt2\). Give your answer in the form \(c+\ln d\), where \(c\) and \(d\) are functions of \(a\).
