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x*e^(-x)

Integral of x*e^(-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo         
  /         
 |          
 |     -x   
 |  x*E   dx
 |          
/           
0           
$$\int\limits_{0}^{\infty} e^{- x} x\, dx$$
Integral(x*E^(-x), (x, 0, oo))
Detail solution
  1. Let .

    Then let and substitute :

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. The integral of the exponential function is itself.

      Now evaluate the sub-integral.

    2. The integral of the exponential function is itself.

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                          
 |                           
 |    -x           -x      -x
 | x*E   dx = C - e   - x*e  
 |                           
/                            
$$\int e^{- x} x\, dx = C - x e^{- x} - e^{- x}$$
The graph
The answer [src]
1
$$1$$
=
=
1
$$1$$
1
The graph
Integral of x*e^(-x) dx

    Use the examples entering the upper and lower limits of integration.