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MHT CET2019Evening ShiftMathematicsIndefinite IntegrationActual

∫ x 2 + 1 x 4 - x 2 + 1 d x =

Options

  1. At a n - 1 x 2 + 1 2 + c
  2. Bt a n - 1 x 2 + c
  3. Ct a n - 1 2 x 2 - 1 + c
  4. Dt a n - 1 x 2 - 1 x + c

Correct answer

D. t a n - 1 x 2 - 1 x + c

Step-by-step solution

Let l = ∫ x 2 + 1 x 4 - x 2 + 1 d x = ∫ 1 + 1 x 2 x 2 - 1 + 1 x 2 d x = ∫ 1 + 1 x 2 x - 1 x + 1 Put x - 1 x = t 1 + 1 x 2 d x = d t ∴ l = ∫ d t t 2 + 1 = t a n - 1 t + c = t a n - 1 x - 1 x + c = t a n - 1 x 2 - 1 x + c

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