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Integral of d{x}:
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Integral of x^2*e^(-x)
Integral of x*exp(-x^2)
Identical expressions
e^(-x^ two)*xdx
e to the power of ( minus x squared ) multiply by xdx
e to the power of ( minus x to the power of two) multiply by xdx
e(-x2)*xdx
e-x2*xdx
e^(-x²)*xdx
e to the power of (-x to the power of 2)*xdx
e^(-x^2)xdx
e(-x2)xdx
e-x2xdx
e^-x^2xdx
Similar expressions
e^(x^2)*xdx

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

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

The solution

You have entered [src]

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

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

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

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   
 | E   *x 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
1   e  
- - ---
2    2

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

=

     -1
1   e  
- - ---
2    2

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

1/2 - exp(-1)/2

Numerical answer [src]

0.316060279414279

0.316060279414279

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