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JEE Main2017MathematicsIndefinite IntegrationActual

If f 3 x - 4 3 x + 4 = x + 2 , x ≠ - 4 3 , and ∫ f x d x = A log 1 - x + B x + C , then the ordered pair A , B is equal to

Options

  1. A- 8 3 , - 2 3
  2. B- 8 3 , 2 3
  3. C8 3 , 2 3
  4. D8 3 , - 2 3

Correct answer

B. - 8 3 , 2 3

Step-by-step solution

Given f 3 x - 4 3 x + 4 = x + 2 ,   x ≠ - 4 3 Let, 3 x - 4 3 x + 4 = t 3 x - 4 = 3 t x + 4 t x = 4 t + 4 3 - 3 t + 2 ∴ f t = 10 - 2 t 3 - 3 t ⇒ f x = 2 x - 10 3 x - 3 ∫ f x d x = ∫ 2 x - 10 3 x - 3 d x = ∫ 2 x 3 x - 3 d x - 10 ∫ d x 3 x - 3 = 2 x 3 - 8 3 ln x - 1 + C , where C is the constant of integration.

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