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Identical expressions
x×e^(-x^ two)
x×e to the power of ( minus x squared )
x×e to the power of ( minus x to the power of two)
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^(-x^2)dx
Similar expressions
x×e^(x^2)

Solving integrals/ x×e^(-x^2)

Integral of x×e^(-x^2) dx

The solution

You have entered [src]

 oo          
  /          
 |           
 |       2   
 |     -x    
 |  x*E    dx
 |           
/            
0

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

Integral(x*E^(-x^2), (x, 0, oo))

Detail solution

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

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

$\int \left(- \frac{e^{u}}{2}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $- \frac{e^{u}}{2}$
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    dx = C - ----
 |                  2  
/

$$\int e^{- x^{2}} x\, dx = C - \frac{e^{- x^{2}}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/2

$$\frac{1}{2}$$

=

1/2

$$\frac{1}{2}$$

1/2

The graph

Integral of x×e^(-x^2) dx

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