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xe^(-x^ two)dx
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Similar expressions
xe^(x^2)dx

Solving integrals/ xe^(-x^2)dx

Integral of xe^(-x^2)dx dx

The solution

You have entered [src]

  1            
  /            
 |             
 |       2     
 |     -x      
 |  x*e   *1 dx
 |             
/              
0

$$\int\limits_{0}^{1} x e^{- x^{2}} \cdot 1\, dx$$

Integral(x*1/E^(1*x^2), (x, 0, 1))

Detail solution

Let $u = e^{- x^{2}}$ .

Then let $du = - 2 x e^{- x^{2}} dx$ and substitute $- \frac{du}{2}$ :

$\int \frac{1}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{1}{2}\right)\, du = - \frac{\int 1\, du}{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  So, the result is: $- \frac{u}{2}$
Now substitute $u$ back in:

$- \frac{e^{- x^{2}}}{2}$
Add the constant of integration:

$- \frac{e^{- x^{2}}}{2}+ \mathrm{constant}$

The answer is:

$- \frac{e^{- x^{2}}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                      2
 |      2             -x 
 |    -x             e   
 | x*e   *1 dx = C - ----
 |                    2  
/

$$-{{e^ {- x^2 }}\over{2}}$$

Simplify

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Plot the graph f(x)

The answer [src]

     -1
1   e  
- - ---
2    2

$${{1}\over{2}}-{{e^ {- 1 }}\over{2}}$$

     -1
1   e  
- - ---
2    2

$$\frac{1}{2} - \frac{1}{2 e}$$

Упростить

Numerical answer [src]

0.316060279414279

0.316060279414279

The graph

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

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Integral of xe^(-x^2)dx dx

Limits of integration:

The graph:

Piecewise:

The solution