Express $\frac{8x + 13}{(1 + 2x)(2 + x)^2}$ in partial fractions.[5] Hence, evaluate \(\int_{1}^{2

Question

Express $\frac{8x + 13}{(1 + 2x)(2 + x)^2}$ in partial fractions.[5] Hence, evaluate $\int_{1}^{2} \frac{8x + 13}{(1 + 2x)(2 + x)^2} \,\mathrm{d}x$.[3]

Accepted Answer

(a) $ \frac{4}{(1 + 2x)} - \frac{2}{(2 + x)} + \frac{1}{(2 + x)^2} $ (b) $ 2\ln{\frac{5}{4}} + \frac{1}{12} $

2024 FMSS PRELIMS P1 Q6

2024 FMSS PRELIMS P1 Q6