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MHT CET202310 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

If I = d x x^2 (x^4+1 )^ 3 4 , then I is

Options

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

Correct answer

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

Step-by-step solution

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

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