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AP EAMCET202023 Sep 2020Morning ShiftMathematicsIndefinite IntegrationActual

∫ x n - 1 x 2 n + 4 d x =

Options

  1. A1 2 n tan - 1 x n 2 + c
  2. Bn 2 tan - 1 x n 2 + c
  3. Cn 2 sin - 1 x n 2 + c
  4. D1 n tan - 1 x n 2 + c

Correct answer

A. 1 2 n tan - 1 x n 2 + c

Step-by-step solution

∫ x n - 1 x 2 n + 4 d x x n = t ⇒ n x n - 1 d x = d t = 1 n ∫ d t t 2 + 4 = 1 2 n tan - 1 t 2 + c = 1 2 n tan - 1 x n 2 + c

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