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MHT CET20249 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

The value of d x (x+1)^ 3 / 4 (x-2)^ 5 / 4 is equal to

Options

  1. A4 ( x+1 x-2 )^ 1 / 4 + c , where c is a constant of integration.
  2. B4 ( x-2 x-1 )^ 1 / 4 + c , where c is a constant of integration.
  3. C-4 3 ( x-2 x+1 )^ 1 / 4 + c , where c is a constant of integration.
  4. D-4 3 ( x+1 x-2 )^ 1 / 4 + c , where c is a constant of integration.

Correct answer

D. -4 3 ( x+1 x-2 )^ 1 / 4 + c , where c is a constant of integration.

Step-by-step solution

aligned & Let I = d x (x+1)^ 3 4 (x-2)^ 5 4 & = d x ( x+1 x-2 )^ 3 4 (x-2)^2 & aligned Put & x+1 x-2 = t -3 (x-2)^2 ~d x= dt I & =- 1 3 dt t ^ 3 4 & =- 1 3 t ^ 1 4 1 4 + c & =- 4 3 ( x+1 x-2 )^ 1 4 + c aligned aligned

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