imo class 12 indefinite integration

Evaluate: ∫ (ax + b)³ dx

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Evaluate: ∫ (ax + b)³ dx

  • A. 3(ax + b)² + C
  • B. (ax + b)⁴ / 4 + C
  • C. (ax + b)⁴ / (4a) + C
  • D. (ax + b)⁴ / a + C

Answer: C) (ax + b)⁴ / (4a) + C

Explanation: Using linear substitution, ∫ (ax + b)ⁿ dx = (ax + b)^(n+1) / (a(n+1)) + C.

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