imo class 12 indefinite integration

Evaluate: ∫ (√x + 1/√x) dx

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Evaluate: ∫ (√x + 1/√x) dx

  • A. (2/3)x^(3/2) + 2x^(1/2) + C
  • B. (3/2)x^(3/2) + (1/2)x^(1/2) + C
  • C. (2/3)x^(3/2) - 2x^(1/2) + C
  • D. x^(3/2) + x^(1/2) + C

Answer: A) (2/3)x^(3/2) + 2x^(1/2) + C

Explanation: ∫ (x^(1/2) + x^(-1/2)) dx = x^(3/2)/(3/2) + x^(1/2)/(1/2) + C = (2/3)x^(3/2) + 2x^(1/2) + C.

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