0606 P13 - Jun 2022 - Q10 - 8 marks
7811
(a) Show that
\(\frac{6}{2+3x}+\frac{4}{(x+1)^2}-\frac{2}{x+1}\)
can be written as
\(\frac{14x+10}{(2+3x)(x+1)^2}.\)
(b) Hence find the exact value of
\(\int_0^2 \frac{14x+10}{(2+3x)(x+1)^2}\,dx.\)
Give your answer in the form \(p+\ln q\), where \(p\) and \(q\) are rational numbers.
