imo class 12 indefinite integration

Evaluate: ∫ (eˣ (1 + x log x) / x) dx

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Evaluate: ∫ (eˣ (1 + x log x) / x) dx

  • A. eˣ log x + C
  • B. eˣ / x + C
  • C. eˣ (log x + x) + C
  • D. eˣ log|x| + eˣ + C

Answer: A) eˣ log x + C

Explanation: Rewriting as ∫ eˣ (1/x + log x) dx. This matches ∫ eˣ (f'(x) + f(x)) dx where f(x) = log x. Result is eˣ f(x) = eˣ log x + C.

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