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MHT CET202410 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

The value of d x x^2 (x^4+1 )^ 3 4 is

Options

  1. A( -x^4+1 x^4 )^ 1 4 + c , where c is constant of integration.
  2. B(x^4+1 )^ 1 4 + c , where c is constant of integration.
  3. C- (x^4+1 )^ 1 4 + c , where c is constant of integration.
  4. D- ( x^4+1 x^4 )^ 1 4 + c , where c is constant of integration.

Correct answer

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

Step-by-step solution

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

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