Question 6 - A-Level Maths

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2011
Session	June
Topic	Standard Integrals and Reverse Chain Rule

Find \(\int 4 \mathrm { e } ^ { x } \left( 3 + \mathrm { e } ^ { 2 x } \right) \mathrm { d } x\).
Show that \(\int _ { - \frac { 1 } { 4 } \pi } ^ { \frac { 1 } { 4 } \pi } \left( 3 + 2 \tan ^ { 2 } \theta \right) \mathrm { d } \theta = \frac { 1 } { 2 } ( 8 + \pi )\).