CAIE P3 2002 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2002
SessionJune
TopicIntegration with Partial Fractions
6 Let \(\mathrm { f } ( x ) = \frac { 4 x } { ( 3 x + 1 ) ( x + 1 ) ^ { 2 } }\).
  1. Express \(f ( x )\) in partial fractions.
  2. Hence show that \(\int _ { 0 } ^ { 1 } \mathrm { f } ( x ) \mathrm { d } x = 1 - \ln 2\).
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