9709 P3 - Jun 2005 - Q4
1701
(i) Use the substitution \(x = \tan \theta\) to show that
\(\int \frac{1-x^2}{(1+x^2)^2} \, dx = \int \cos 2\theta \, d\theta.\)
(ii) Hence find the value of
\(\int_0^1 \frac{1-x^2}{(1+x^2)^2} \, dx.\)
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