CAIE P3 2016 March — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionMarch
TopicIntegration with Partial Fractions

9 Let \(\mathrm { f } ( x ) = \frac { 3 x ^ { 3 } + 6 x - 8 } { x \left( x ^ { 2 } + 2 \right) }\).
  1. Express \(\mathrm { f } ( x )\) in the form \(A + \frac { B } { x } + \frac { C x + D } { x ^ { 2 } + 2 }\).
  2. Show that \(\int _ { 1 } ^ { 2 } \mathrm { f } ( x ) \mathrm { d } x = 3 - \ln 4\).