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) $\dfrac4{1+2x}-\dfrac2{x+2}+\dfrac1{(x+2)^2}$ (b) $2\ln\left(\dfrac54\right)+\dfrac1{12}$

2024 FMSS PRELIMS P1 Q6

2024 FMSS PRELIMS P1 Q6

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