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Integral of d{x}:
Integral of x/y
Integral of exp(2x)
Integral of dx/(1+e^x)
Integral of 1/(1+x^2)^1/2
Identical expressions
x*exp(two x^2)
x multiply by exponent of (2x squared )
x multiply by exponent of (two x squared )
x*exp(2x2)
x*exp2x2
x*exp(2x²)
x*exp(2x to the power of 2)
xexp(2x^2)
xexp(2x2)
xexp2x2
xexp2x^2
x*exp(2x^2)dx

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

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

The solution

You have entered [src]

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

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

Integral(x*exp(2*x^2), (x, 0, 1))

Detail solution

Let $u = 2 x^{2}$ .

Then let $du = 4 x dx$ and substitute $\frac{du}{4}$ :

$\int \frac{e^{u}}{4}\, du$
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: $\frac{e^{u}}{4}$
Now substitute $u$ back in:

$\frac{e^{2 x^{2}}}{4}$
Add the constant of integration:

$\frac{e^{2 x^{2}}}{4}+ \mathrm{constant}$

The answer is:

$\frac{e^{2 x^{2}}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                      2
 |       2           2*x 
 |    2*x           e    
 | x*e     dx = C + -----
 |                    4  
/

$$\int x e^{2 x^{2}}\, dx = C + \frac{e^{2 x^{2}}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$- \frac{1}{4} + \frac{e^{2}}{4}$$

$$- \frac{1}{4} + \frac{e^{2}}{4}$$

-1/4 + exp(2)/4

Numerical answer [src]

1.59726402473266

1.59726402473266

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

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The solution