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AP EAMCET202319 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

If f(x)= x (1+n x^n )^ 1 / n for n 2 , then x^ n-2 f(x) d x=

Options

  1. A1 n(n-1) (1+n x^n )^ 1- 1 n +C
  2. B1 (n-1) (1+n x^n )^ 1- 1 n +C
  3. C1 n(n-1) (1+n x^n )^ 1+ 1 n +C
  4. D1 n+1 (1+n x^n )^ 1+ 1 n +C

Correct answer

A. 1 n(n-1) (1+n x^n )^ 1- 1 n +C

Step-by-step solution

x^ n-2 f(x) d x= x^ n-1 (1+n x^n )^ 1 / n d x Let 1+n x n= t x^ n-1 d x= 1 n^2 d t aligned & = 1 n^2 d t t^ 1 / n = 1 n^2 t^ -1 / n +1 (- 1 n +1 ) +C & = 1 n(n-1) (1+n x^n )^ 1- 1 n +C aligned

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