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JEE Main2015MathematicsIndefinite IntegrationActual

The integral ∫ d x x 2 x 4 + 1 3 4 equals to

Options

  1. A- x 4 + 1 x 4 1 4 + c
  2. Bx 4 + 1 x 4 1 4 + c
  3. Cx 4 + 1 1 4 + c
  4. D- x 4 + 1 1 4 + c

Correct answer

A. - x 4 + 1 x 4 1 4 + c

Step-by-step solution

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

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