MHT CET202416 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
The integral 2 x^3-1 x^4+x ~d x is equal to
Options
- A|x^3+1 | x^2 + c , (where c is a constant of integration)
- B1 2 (x^3+1 )^2 |x^3 | + c ; (where c is a constant of integration)
- C| x^3+1 x |+ c , (where c is a constant of integration)
- 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