imo class 12 indefinite integration

Evaluate: ∫ sec⁴ x tan x dx

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Evaluate: ∫ sec⁴ x tan x dx

  • A. sec⁴ x / 4 + C
  • B. tan⁴ x / 4 + C
  • C. sec⁵ x / 5 + C
  • D. sec³ x / 3 + C

Answer: A) sec⁴ x / 4 + C

Explanation: Let sec x = t, sec x tan x dx = dt. Integral is ∫ t³ dt = t⁴/4 + C = sec⁴ x / 4 + C.

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