9709 P3 - Jun 2008 - Q7
2087
Let \(f(x) \equiv \frac{x^2 + 3x + 3}{(x+1)(x+3)}\).
(i) Express \(f(x)\) in partial fractions.
(ii) Hence show that \(\int_0^3 f(x) \, dx = 3 - \frac{1}{2} \ln 2\).
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