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xe^(x^2)

Integral of xe^(x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |     / 2\   
 |     \x /   
 |  x*E     dx
 |            
/             
0             
$$\int\limits_{0}^{1} e^{x^{2}} x\, dx$$
Integral(x*E^(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\           \x /
 |    \x /          e    
 | x*E     dx = C + -----
 |                    2  
/                        
$$\int e^{x^{2}} x\, dx = C + \frac{e^{x^{2}}}{2}$$
The graph
The answer [src]
  1   E
- - + -
  2   2
$$- \frac{1}{2} + \frac{e}{2}$$
=
=
  1   E
- - + -
  2   2
$$- \frac{1}{2} + \frac{e}{2}$$
-1/2 + E/2
Numerical answer [src]
0.859140914229523
0.859140914229523
The graph
Integral of xe^(x^2) dx

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