9709 P32 - Jun 2019 - Q8
2101
Let \(f(x) = \frac{10x + 9}{(2x + 1)(2x + 3)^2}\).
(i) Express \(f(x)\) in partial fractions.
(ii) Hence show that \(\int_0^1 f(x) \, dx = \frac{1}{2} \ln \frac{9}{5} + \frac{1}{5}\).
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