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NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice

If I n = ∫ ln ⁡ x n d x , then I 10 + 10 I 9 is equal to (where C is the constant of integration)

Options

  1. Ax ln ⁡ x 10 + C
  2. B10 ln ⁡ x 9 + C
  3. C9 ln ⁡ x 10 + C
  4. Dx ln ⁡ x 9 + C

Correct answer

A. x ln ⁡ x 10 + C

Step-by-step solution

I n = ∫ ln ⁡ x n d x I n = x ln ⁡ x n - ∫ x n ln ⁡ x n - 1 x d x Ι n = x ln ⁡ x n - nΙ n - 1 I n + n I n - 1 = x ln ⁡ x n + C I 10 + 10 I 9 = x ln ⁡ x 10 + C

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