Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20225 Aug 2022Morning ShiftMathematicsIndefinite IntegrationActual

1- x 1+ x d x= (where C is a constant of integration)

Options

  1. A-2 1-x - ⁻¹ x + x(1-x)
  2. B-2 1-x + ⁻¹ x + x(1-x)
  3. C2 1-x + ⁻¹ x + x(1-x)
  4. D-2 1-x + ⁻¹ x - x(1-x)

Correct answer

B. -2 1-x + ⁻¹ x + x(1-x)

Step-by-step solution

aligned & 1- x 1+ x d x= (1- x )^2 1-x d x & 1- x 1-x d x= d x 1-x - x 1-x d x & -2 1-x - ^2 1- ^2 (-2 d ) [ let x= ^2 ] & =-2 1-x + 2 ^2 d & aligned aligned & =-2 1-x + (1+ 2 ) d & =-2 1-x + + 2 2 +C & =-2 1-x + + +C & =-2 1-x + ⁻¹ x + 1-x x +C & =-2 1-x + ⁻¹ x + x(1-x) +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