Question 6 - A-Level Maths

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2020
Session	November
Topic	Standard Integrals and Reverse Chain Rule

Find \(\int \left( \frac { 8 } { 4 x + 1 } + \frac { 8 } { \cos ^ { 2 } ( 4 x + 1 ) } \right) \mathrm { d } x\).
It is given that \(\int _ { 0 } ^ { \frac { 1 } { 2 } \pi } \left( 3 + 4 \cos ^ { 2 } \frac { 1 } { 2 } x + k \sin 2 x \right) \mathrm { d } x = 10\). Find the exact value of the constant \(k\).