CAIE P3 2017 June — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2017
SessionJune
TopicIntegration with Partial Fractions

9 Let \(\mathrm { f } ( x ) = \frac { 3 x ^ { 2 } - 4 } { x ^ { 2 } ( 3 x + 2 ) }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Hence show that \(\int _ { 1 } ^ { 2 } \mathrm { f } ( x ) \mathrm { d } x = \ln \left( \frac { 25 } { 8 } \right) - 1\).