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JEE Main2016MathematicsIndefinite IntegrationActual

The integral ∫ d x 1 + x x - x 2 is equal to

Options

  1. A- 2 1 + x 1 - x + c
  2. B- 1 - x 1 + x + c
  3. C- 2   1 - x 1 + x + c
  4. D1 + x 1 - x + c

Correct answer

C. - 2   1 - x 1 + x + c

Step-by-step solution

I = ∫ d x 1 + x x 1 - x Put, 1 + x = t   ⇒ 1 2 x d x = d t And, 1 - x = 1 - t - 1 2 = 2 t - t 2 ∴   I =   ∫ 2 d t t 2 t - t 2 Again put, t = 1 z ⇒ d t = - 1 z 2 d z ⇒ I = 2 ∫ - 1 z 2   d z 1 z   2 z - 1 z 2 = 2 ∫ - d z 2 z - 1 = - 2 2 z - 1 + c Where c is arbitrary constant. = - 2 2 t - 1   + c = - 2 2 - t t + c = - 2   1 - x 1 + x + c

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