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The value of ∫ d x x ( x n + 1 ) is equal to

Options

  1. A1 n log e ( x n x n + 1 ) + c
  2. B1 n log e ( x n + 1 x n ) + c
  3. Clog e ( x n x n + 1 ) + c
  4. DNone of these

Correct answer

A. 1 n log e ( x n x n + 1 ) + c

Step-by-step solution

I= ∫ d x ( 1 + 1 x n ) × x n + 1 put 1 + 1 x n = t − n x n + 1 . d x = d t I = ∫ − d t n t = − 1 n ln | t | + c I = − 1 n ln ( 1 + 1 x n ) + c I = 1 n ln ( x n x n + 1 ) + c

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