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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

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*exp(-3*x^2), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of the exponential function is itself.

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                        
 |                        2
 |        2           -3*x 
 |    -3*x           e     
 | x*e      dx = C - ------
 |                     6   
/
$$\int x e^{- 3 x^{2}}\, dx = C - \frac{e^{- 3 x^{2}}}{6}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     -3
1   e  
- - ---
6    6
$$\frac{1}{6} - \frac{1}{6 e^{3}}$$ 
=
= 
     -3
1   e  
- - ---
6    6
$$\frac{1}{6} - \frac{1}{6 e^{3}}$$ 
1/6 - exp(-3)/6
Numerical answer [src] 
0.158368821938689
0.158368821938689
The graph
Integral of x*exp(-3x^2) dx

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

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