Question 4 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2005
Session	June
Topic	Addition & Double Angle Formulae

Use the substitution $x = \tan \theta$ to show that $$\int \frac { 1 - x ^ { 2 } } { \left( 1 + x ^ { 2 } \right) ^ { 2 } } \mathrm {~d} x = \int \cos 2 \theta \mathrm {~d} \theta$$
Hence find the value of $$\int _ { 0 } ^ { 1 } \frac { 1 - x ^ { 2 } } { \left( 1 + x ^ { 2 } \right) ^ { 2 } } \mathrm {~d} x$$