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x*exp(x^2/2)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1         
  /         
 |          
 |      2   
 |     x    
 |     --   
 |     2    
 |  x*e   dx
 |          
/           
0           
$$\int\limits_{0}^{1} x e^{\frac{x^{2}}{2}}\, dx$$
Integral(x*exp(x^2/2), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of a constant is the constant times the variable of integration:

      Now substitute back in:

    Method #2

    1. Let .

      Then let and substitute :

      1. The integral of the exponential function is itself.

      Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                  
 |                   
 |     2            2
 |    x            x 
 |    --           --
 |    2            2 
 | x*e   dx = C + e  
 |                   
/                    
$$\int x e^{\frac{x^{2}}{2}}\, dx = C + e^{\frac{x^{2}}{2}}$$
The graph
The answer [src]
      1/2
-1 + e   
$$-1 + e^{\frac{1}{2}}$$
=
=
      1/2
-1 + e   
$$-1 + e^{\frac{1}{2}}$$
-1 + exp(1/2)
Numerical answer [src]
0.648721270700128
0.648721270700128
The graph
Integral of x*exp(x^2/2) dx

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