Question 4 - A-Level Maths

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2017
Session	November
Topic	Standard Integrals and Reverse Chain Rule

Find \(\int \frac { 4 + \sin ^ { 2 } \theta } { 1 - \sin ^ { 2 } \theta } \mathrm {~d} \theta\).
Given that \(\int _ { 0 } ^ { a } \frac { 2 } { 3 x + 1 } \mathrm {~d} x = \ln 16\), find the value of the positive constant \(a\).