CAIE P3 2019 November — Question 8

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2019
SessionNovember
TopicIntegration with Partial Fractions

8 Let \(\mathrm { f } ( x ) = \frac { 2 x ^ { 2 } + x + 8 } { ( 2 x - 1 ) \left( x ^ { 2 } + 2 \right) }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Hence, showing full working, find \(\int _ { 1 } ^ { 5 } \mathrm { f } ( x ) \mathrm { d } x\), giving the answer in the form \(\ln c\), where \(c\) is an integer.