(i)[4]
Write $f(x)$ in the form $\dfrac{A}{2 - x} + \dfrac{Bx + C}{4 + x^2}$.
(ii)[5]
Show that $\int_0^1 f(x)\,dx$ is equal to $\ln\!\left(\tfrac{25}{2}\right)$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Define $f(x)$ by $\dfrac{12 + 8x - x^2}{(2 - x)(4 + x^2)}$.