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The value of the integral Ι = ∫ 2 x 9 + x 10 x 2 + x 3 3 d x is equal to (where, C is the constant of integration)

Options

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

Correct answer

A. x 4 2 1 + x 2 + C

Step-by-step solution

Taking x 12 common from denominator, Ι = ∫ 2 x - 3 + x - 2 x - 2 + x - 1 3 d x Let, x - 2 + x - 1 = t ⇒ - 2 x - 3 - x - 2 d x = d t ∴ Ι = - ∫ d t t 3 = t - 2 2 + C = 1 2 x - 2 + x - 1 2 + C = x 4 2 1 + x 2 + C

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