Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202310 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

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

Options

  1. A2 2- 2 x^2 + 1 x^4 + c , where c is a constant of integration.
  2. B2 2+ 2 x^2 + 1 x^4 + c , where c is a constant of integration.
  3. C1 2 2- 2 x^2 + 1 x^4 + c , where c is a constant of integration.
  4. D2 2- 2 x^2 - 1 x^4 + c , where c is a constant of integration.

Correct answer

C. 1 2 2- 2 x^2 + 1 x^4 + c , where c is a constant of integration.

Step-by-step solution

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

Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

If 5 x x -2 dx = ax + b | x -2 x |+ c , then a + b = 2025x Cos ⁻¹ ( 1-x^2 1+x^2 ) d x(x>0)= 2025d x (1+ x ) x-x^2 = 2025If x x x+1 ~d x= f (x)+ k , then f ( 4 )= 2025If x^4+1 x^2+1 d x=A x^3+B x^2+C x+D Tan ⁻¹ x+E , then A+B+C+D= 2025If x^2-x+2 x^2+x+2 d x=x- (f(x))+ 2 7 Tan ⁻¹(g(x))+c , then f (-1)+ 7 ~g (-1)= 2025(x- 3 ) (x+ 6 ) d x= 2025If a x+3 x 5 x+2 x d x= 26 29 x- k 29 |5 x+2 x|+c , then |a+k|= 2025 Full Indefinite Integration list All MHT CET PYQs