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8 marksIntegration II

CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2 · Question 2(a)(i)

Determine the integral of x^5 cos(x^3) dx.

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Other parts of this question

  1. 2(a)(ii)Determine the integral of e^(2x) / sqrt(1 - e^(4x)) dx.[5 marks]
  2. 2(b)(i)Use partial fractions to show that (x^4 + 1) / (x(x^2 + 1)^2) = 1/x - 2x / (x^2 + 1)^2.[8 marks]
  3. 2(b)(ii)Hence, determine the integral of (x^4 + 1) / (x(x^2 + 1)^2) dx.[4 marks]

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