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WAEC Further Mathematics 2014 Question 22

Question 22

Integration

Integrate (x − 1/x)2 with respect to x.

  1. A.(1/3)(x − 1/x)3 + C
  2. B.x3/3 − x − 1/x3 + C
  3. C.x3/3 − 2x + 1/x3 + C
  4. D.x3/3 − 2x − 1/x + C
Show the answer and explanation

Answer: D (x3/3 − 2x − 1/x + C)

Explanation

(x − 1/x)² = x² − 2 + x⁻². Integrating: x³/3 − 2x − 1/x + C.