imo class 12 indefinite integration

Evaluate: ∫ x² eˣ dx

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Evaluate: ∫ x² eˣ dx

  • A. eˣ(x² - 2x + 2) + C
  • B. eˣ(x² + 2x + 2) + C
  • C. eˣ(x² - 2x) + C
  • D. eˣ x² / 2 + C

Answer: A) eˣ(x² - 2x + 2) + C

Explanation: Applying integration by parts twice yields x² eˣ - 2x eˣ + 2eˣ + C = eˣ(x² - 2x + 2) + C.

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