Integral of xe^x² dx

The solution

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  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

Let $u = x^{2}$ .

Then let $du = 2 x dx$ and substitute $\frac{du}{2}$ :

$\int \frac{e^{u}}{2}\, du$
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  
/

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

Simplify

The graph

Plot the graph f(x)

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

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

Other calculators

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Identical expressions

Integral of xe^x² dx

Limits of integration:

The graph:

Piecewise:

The solution