(i)[5]
Write $f(x)$ as partial fractions.
(ii)[5]
Hence, showing all necessary working, show that $\displaystyle \int_{-1}^{0} f(x)\,dx = 1 + \tfrac{1}{2}\ln\left(\tfrac{3}{4}\right)$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Define $f(x)=\frac{6x^2 + 8x + 9}{(2 - x)(3 + 2x)^2}$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or indicate the form $\frac{A}{2-x}+\frac{B}{3+2x}+\frac{C}{(3+2x)^2}$” …
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