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8 marksIntegration II

CAPE Pure Mathematics Unit 2 · May/June 2021 · Paper 2 · Question 2(a)

Using the substitution eˣ = 3 cos θ, or otherwise, determine ∫ eˣ √(9-e²ˣ) dx.

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  1. 2(b)(i)Use partial fractions to prove that (2x + 1) / (2x³ - x² + 8x - 4) = 8 / (17(2x - 1)) - (4x - 15) / (17(x² + 4)).[12 marks]
  2. 2(b)(ii)Hence, find ∫ (2x + 1) / (2x³ - x² + 8x - 4) dx.[5 marks]

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