Mister Exam

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Integral of d{x}:
Integral of a
Integral of e^2x
Integral of -1/t
Integral of x/y
Limit of the function:
x*exp(-x^2)
Derivative of:
x*exp(-x^2)
Identical expressions
x*exp(-x^ two)
x multiply by exponent of ( minus x squared )
x multiply by exponent of ( minus x to the power of two)
x*exp(-x2)
x*exp-x2
x*exp(-x²)
x*exp(-x to the power of 2)
xexp(-x^2)
xexp(-x2)
xexp-x2
xexp-x^2
x*exp(-x^2)dx
Similar expressions
x*exp(x^2)

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

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

The solution

You have entered [src]

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

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

Integral(x*exp(-x^2), (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   
 | x*e    dx = C - ----
 |                  2  
/

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

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

The graph

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

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