CAIE P3 2021 June — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionJune
TopicIntegration with Partial Fractions

4 Let \(f ( x ) = \frac { 15 - 6 x } { ( 1 + 2 x ) ( 4 - x ) }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Hence find \(\int _ { 1 } ^ { 2 } \mathrm { f } ( x ) \mathrm { d } x\), giving your answer in the form \(\ln \left( \frac { a } { b } \right)\), where \(a\) and \(b\) are integers.