9709 P31 - Nov 2011 - Q8
2112
Let \(f(x) = \frac{12 + 8x - x^2}{(2-x)(4+x^2)}\).
(i) Express \(f(x)\) in the form \(\frac{A}{2-x} + \frac{Bx+C}{4+x^2}\).
(ii) Show that \(\int_0^1 f(x) \, dx = \ln\left(\frac{25}{2}\right)\).
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