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Identical expressions
x*e^(-3x^ two)
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x multiply by e to the power of ( minus 3x to the power of two)
x*e(-3x2)
x*e-3x2
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xe^(-3x^2)
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Similar expressions
x*e^(3x^2)

Solving integrals/ x*e^(-3x^2)

Integral of x*e^(-3x^2) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |         2   
 |     -3*x    
 |  x*e      dx
 |             
/              
0

$$\int\limits_{0}^{1} x e^{- 3 x^{2}}\, dx$$

Integral(x/E^(3*x^2), (x, 0, 1))

Detail solution

Let $u = e^{- 3 x^{2}}$ .

Then let $du = - 6 x e^{- 3 x^{2}} dx$ and substitute $- \frac{du}{6}$ :

$\int \frac{1}{36}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{1}{6}\right)\, du = - \frac{\int 1\, du}{6}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  So, the result is: $- \frac{u}{6}$
Now substitute $u$ back in:

$- \frac{e^{- 3 x^{2}}}{6}$
Add the constant of integration:

$- \frac{e^{- 3 x^{2}}}{6}+ \mathrm{constant}$

The answer is:

$- \frac{e^{- 3 x^{2}}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                        2
 |        2           -3*x 
 |    -3*x           e     
 | x*e      dx = C - ------
 |                     6   
/

$$-{{e^ {- 3\,x^2 }}\over{6}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     -3
1   e  
- - ---
6    6

$${{1}\over{6}}-{{e^ {- 3 }}\over{6}}$$

     -3
1   e  
- - ---
6    6

$$- \frac{1}{6 e^{3}} + \frac{1}{6}$$

Simplify

Numerical answer [src]

0.158368821938689

0.158368821938689

The graph

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

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Identical expressions

Similar expressions

Integral of x*e^(-3x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution