CAIE P3 2022 June — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2022
SessionJune
TopicIntegration with Partial Fractions

8 Let \(\mathrm { f } ( x ) = \frac { x ^ { 2 } + 9 x } { ( 3 x - 1 ) \left( x ^ { 2 } + 3 \right) }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Hence find \(\int _ { 1 } ^ { 3 } \mathrm { f } ( x ) \mathrm { d } x\), giving your answer in a simplified exact form.