Edexcel P4 2022 January — Question 4

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2022
SessionJanuary
TopicIntegration with Partial Fractions

4. $$\mathrm { f } ( x ) = \frac { 4 - 4 x } { x ( x - 2 ) ^ { 2 } } \quad x > 2$$
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Hence find \(\int \mathrm { f } ( x ) \mathrm { d } x\)
  3. Find $$\int _ { 3 } ^ { 5 } f ( x ) d x$$ giving your answer in the form \(a + \ln b\), where \(a\) and \(b\) are rational numbers to be found.