2026 HGV P2 Q5

2026 HGV P2 Q5

Secondary 4
9 marks
  1. Express \(\dfrac{2x+8}{(x^2+4)(x-1)}\) in partial fractions.[6]
  2. Hence, evaluate \(\displaystyle\int_2^3\dfrac{x+4}{(x^2+4)(x-1)}\,\mathrm{d}x\).[3]

Solution:

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Answer:(a) \(-\dfrac{2x}{x^2+4}+\dfrac2{x-1}\). (b) \(\dfrac12\ln\dfrac{32}{13}\approx0.450\).

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