Mister Exam

Integral of xexp(-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1         
  /         
 |          
 |     -x   
 |  x*e   dx
 |          
/           
0           
$$\int\limits_{0}^{1} x e^{- x}\, dx$$
Integral(x*exp(-x), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    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:

    Method #2

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. Let .

        Then let and substitute :

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. The integral of the exponential function is itself.

          So, the result is:

        Now substitute back in:

      Now evaluate the sub-integral.

    2. The integral of a constant times a function is the constant times the integral of the function:

      1. Let .

        Then let and substitute :

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. The integral of the exponential function is itself.

          So, the result is:

        Now substitute back in:

      So, the result is:

  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  
 |                           
/                            
$$\int x e^{- x}\, dx = C - x e^{- x} - e^{- x}$$
The graph
The answer [src]
       -1
1 - 2*e  
$$1 - \frac{2}{e}$$
=
=
       -1
1 - 2*e  
$$1 - \frac{2}{e}$$
1 - 2*exp(-1)
Numerical answer [src]
0.264241117657115
0.264241117657115
The graph
Integral of xexp(-x) dx

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