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Identical expressions
e^(-x^ two)*x
e to the power of ( minus x squared ) multiply by x
e to the power of ( minus x to the power of two) multiply by x
e(-x2)*x
e-x2*x
e^(-x²)*x
e to the power of (-x to the power of 2)*x
e^(-x^2)x
e(-x2)x
e-x2x
e^-x^2x
e^(-x^2)*xdx
Similar expressions
e^(x^2)*x

Solving integrals/ e^(-x^2)*x

Integral of e^(-x^2)*x dx

The solution

You have entered [src]

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

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

Integral(x/E^(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   
 | e   *x dx = C - ----
 |                  2  
/

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

Simplify

The graph

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

Integral of e^(-x^2)*x dx

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