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MHT CET20242 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

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

Options

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

Correct answer

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

Step-by-step solution

aligned & 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 & 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 aligned

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