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MHT CET202310 May 2023Evening 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 a constant of integration.
  2. B(x^4+1 )^ 1 4 + c , where c is a constant of integration.
  3. C- (x^4+1 )^ 1 4 + c , where c is a constant of integration.
  4. D- ( x^4+1 x^4 )^ 1 4 + c , where c is a constant of integration.

Correct answer

D. - ( x^4+1 x^4 )^ 1 4 + 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 ~d x= dt aligned I & =- 1 4 d t t^ 3 4 & =- 1 4 4 t^ 1 4 +c=-t^ 1 4 +c & =- (1+ 1 x^4 )^ 1 4 +c=- ( x^4+1 x^4 )^ 1 4 +c aligned

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