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NDA2024MathematicsIndefinite IntegrationActual

Let d x x+1 - x-1 = (x+1)^ 3 2 + (x-1)^ 3 2 +c What is the value of ?

Options

  1. A- 2 3
  2. B- 1 3
  3. C1 3
  4. D2 3

Correct answer

C. 1 3

Step-by-step solution

Given, d x x+1 - x-1 = (x+1)^ 3 2 + (x-1)^ 3 2 +c ....(i) Let, I = d x x+1 - x-1 aligned & = ( x+1 + x-1 ) d x ( x+1 - x-1 )( x+1 + x-1 ) & I = 1 2 (x+1) d x+ 1 2 x-1 d x & I = 1 2 (x+1)^ 3 2 ( 3 2 ) + 1 2 (x-1)^ 3 2 ( 3 2 ) +c & I = 1 3 (x+1)^ 3 2 + 1 3 (x-1)^ 3 2 +c & d x x+1 - x-1 = 1 3 (x+1)^ 3 2 + 1 3 (x-1)^ 3 2 +c (ii) aligned From (i) and (ii) we get = 1 3

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