Question 6 - A-Level Maths

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2018
Session	November
Topic	Standard Integrals and Reverse Chain Rule

Show that \(\int _ { 1 } ^ { 6 } \frac { 12 } { 3 x + 2 } \mathrm {~d} x = \ln 256\).
Find the exact value of \(\int _ { 0 } ^ { \frac { 1 } { 6 } \pi } \left( 8 \sin ^ { 2 } x + \tan ^ { 2 } 2 x \right) \mathrm { d } x\), showing all necessary working.