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MHT CET202416 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

The integral 2 x^3-1 x^4+x ~d x is equal to

Options

  1. A|x^3+1 | x^2 + c , (where c is a constant of integration)
  2. B1 2 (x^3+1 )^2 |x^3 | + c ; (where c is a constant of integration)
  3. C| x^3+1 x |+ c , (where c is a constant of integration)
  4. D1 2 |x^3+1 | x^2 + c , (where c is a constant of integration)

Correct answer

C. | x^3+1 x |+ c , (where c is a constant of integration)

Step-by-step solution

Let I= 2 x^3-1 x^4+x ~d x= (2 x- 1 x^2 ) (x^2+ 1 x ) d x .[Dividing N ^ r and D ^ r by x^2 ] Put x^2+ 1 x = t (2 x- 1 x^2 ) d x= dt aligned I & = d t t & = |t|+c & = |x^2+ 1 x |+c= | x^3+1 x |+c aligned

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