Let $\mathrm{f}(x) = \frac{3 - 3x^2}{(2x + 1)(x + 2)^2}$. Express $\mathrm{f}(x)$ in partia

Question

Let $\mathrm{f}(x) = \frac{3 - 3x^2}{(2x + 1)(x + 2)^2}$. Express $\mathrm{f}(x)$ in partial fractions.[5] Hence find the value of $\int_{0}^{4} \mathrm{f}(x) \; \mathrm{d}x$, giving your answer in the form $a + b \ln c$, where $a$, $b$ and $c$ are integers.[5]

Accepted Answer

(a) $ \frac{1}{2x+1} - \frac{2}{x+2} + \frac{3}{(x + 2)^2} $ (b) $1 - \ln{3}$

2024 CGSS P2 Q2

2024 CGSS P2 Q2