imo class 12 indefinite integration

Evaluate: ∫ eˣ (tan x + sec² x) dx

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Evaluate: ∫ eˣ (tan x + sec² x) dx

  • A. eˣ tan x + C
  • B. eˣ sec² x + C
  • C. eˣ sec x + C
  • D. eˣ log|sec x| + C

Answer: A) eˣ tan x + C

Explanation: Form is ∫ eˣ [f(x) + f'(x)] dx with f(x) = tan x and f'(x) = sec² x. Result is eˣ tan x + C.

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