imo class 12 indefinite integration

Evaluate: ∫ x sec² x dx

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Evaluate: ∫ x sec² x dx

  • A. x tan x - log|sec x| + C
  • B. x tan x + log|sec x| + C
  • C. x sec x - tan x + C
  • D. x tan x - log|cos x| + C

Answer: A) x tan x - log|sec x| + C

Explanation: By parts: u = x, dv = sec² x dx. v = tan x. uv - ∫ v du = x tan x - ∫ tan x dx = x tan x - log|sec x| + C.

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