Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20244 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

(1+x- 1 x ) e ^ x+ 1 x ~d x equal to

Options

  1. A(x+1) e ^ x+ 1 x + c , (where c is a constant of integration)
  2. B-x e ^ x+ 1 x + c , (where c is a constant of integration)
  3. C(x-1) e ^ x+ 1 x + c , (where c is a constant of integration)
  4. Dx e ^ x+ 1 x + c , (where c is a constant of integration)

Correct answer

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

Step-by-step solution

Note that [x f ^ (x)+ f (x) ] d x=x f (x)+ c aligned & (1+x- 1 x ) e ^ x+ 1 x ~d x & = [x e ^ x+ 1 x (1- 1 x^2 )+ e ^ x+ 1 x ] d x & =x e ^ 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