(a)[5]
Express $f(x)$ as a sum of partial fractions.
(b)[5]
Hence find $\int_{1}^{3} f(x)\,dx$, giving the exact answer in fully simplified form.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Define $f(x)$ by $f(x) = \dfrac{x^2 + 9x}{(3x - 1)(x^2 + 3)}$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State, or make clear by implication, the form $\dfrac{A}{3x-1}+\dfrac{Bx+C}{x^2+3}$” …
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