imo class 12 indefinite integration

Evaluate: ∫ log x dx

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Evaluate: ∫ log x dx

  • A. x log x - x + C
  • B. 1/x + C
  • C. log x - x + C
  • D. x log x + x + C

Answer: A) x log x - x + C

Explanation: Integrate by parts: u = log x, dv = 1 dx. du = 1/x dx, v = x. uv - ∫ v du = x log x - ∫ x(1/x) dx = x log x - x + C.

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