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JEE Main2015MathematicsIndefinite IntegrationActual

The integral ∫ d x x + 1 3 4 x - 2 5 4 , is equal to

Options

  1. A4 x - 2 x + 1 1 4 + c
  2. B- 4 3   x + 1 x - 2 1 4 + c
  3. C4 x + 1 x - 2 1 4 + c
  4. D- 4 3 x - 2 x + 1 1 4 + c

Correct answer

B. - 4 3   x + 1 x - 2 1 4 + c

Step-by-step solution

∫ d x x + 1 3 4 x - 2 5 4 = ∫ d x x + 1 2 x - 2 x + 1 5 4 Put, x - 2 x + 1 = t ⇒ 3 x + 1 2 d x = d t ∴ I = - 4 3 1 t 1 4 + c = - 4 3 x + 1 x - 2 1 4 + c , c being the constant of integration.

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