imo class 12 indefinite integration

Evaluate: ∫ (log x) / x dx

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Evaluate: ∫ (log x) / x dx

  • A. log(log x) + C
  • B. (log x)² / 2 + C
  • C. 1/x² + C
  • D. x log x + C

Answer: B) (log x)² / 2 + C

Explanation: Let log x = t, then (1/x) dx = dt. The integral becomes ∫ t dt = t²/2 + C = (log x)² / 2 + C.

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