Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202311 May 2023Morning ShiftMathematicsIndefinite IntegrationActual

e ^x(1+x) ^2 ( e ^x x ) d x=

Options

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

Correct answer

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

Step-by-step solution

Let I = e ^x(1+x) ^2 ( e ^x x ) d x Put e ^x x= t e ^x(x+1) d x= dt aligned I & = dt ^2 t & = ^2 t d & = t + c I & = (x e ^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