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JEE Main201912 Jan 2019Evening ShiftMathematicsIndefinite IntegrationActual

The integral ∫ 3 x 13 + 2 x 11 2 x 4 + 3 x 2 + 1 4 d x , is equal to

Options

  1. Ax 4 6 2 x 4 + 3 x 2 + 1 3 + C
  2. Bx 4 2 x 4 + 3 x 2 + 1 3 + C
  3. Cx 12 2 x 4 + 3 x 2 + 1 3 + C
  4. Dx 12 6 2 x 4 + 3 x 2 + 1 3 + C

Correct answer

D. x 12 6 2 x 4 + 3 x 2 + 1 3 + C

Step-by-step solution

The given integral can be written as I = ∫ 3 .   x - 3 + 2 x - 5 2 + 3 x - 2 + x - 4 4 d x (Dividing x 16 to both numerator and denominator), Let,   2 + 3 x - 2 + x - 4 = t ⇒ - 6 x - 3 - 4 x - 5 d x = d t ⇒ - 2 3 x - 3 + 2 x - 5 d x = d t ∴ I = - 1 2 ∫ d t t 4 = - 1 2 t - 4 + 1 - 4 + 1 = 1 6 1 t 3 + C , where C is the constant of integration. = 1 6 2 + 3 x - 2 + x - 4 3 + C = x 12 6 2 x 4 + 3 x 2 + 1 3 + C

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