Question 5 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2015
Session	June
Topic	Standard Integrals and Reverse Chain Rule

Find \(\int \left( 4 + \tan ^ { 2 } 2 x \right) \mathrm { d } x\).
Find the exact value of \(\int _ { \frac { 1 } { 4 } \pi } ^ { \frac { 1 } { 2 } \pi } \frac { \sin \left( x + \frac { 1 } { 6 } \pi \right) } { \sin x } \mathrm {~d} x\).