CAIE P3 2015 June — Question 10

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2015
SessionJune
TopicIntegration with Partial Fractions

10 Let \(\mathrm { f } ( x ) = \frac { 11 x + 7 } { ( 2 x - 1 ) ( x + 2 ) ^ { 2 } }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Show that \(\int _ { 1 } ^ { 2 } \mathrm { f } ( x ) \mathrm { d } x = \frac { 1 } { 4 } + \ln \left( \frac { 9 } { 4 } \right)\).