CAIE P2 2016 June — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2016
SessionJune
TopicStandard Integrals and Reverse Chain Rule

7
  1. Find \(\int \frac { 1 + \cos ^ { 4 } 2 x } { \cos ^ { 2 } 2 x } \mathrm {~d} x\).
  2. Without using a calculator, find the exact value of \(\int _ { 4 } ^ { 14 } \left( 2 + \frac { 6 } { 3 x - 2 } \right) \mathrm { d } x\), giving your answer in the form \(\ln \left( a \mathrm { e } ^ { b } \right)\), where \(a\) and \(b\) are integers.