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Identical expressions
two xe^(-x^2)
2xe to the power of ( minus x squared )
two xe to the power of ( minus x squared )
2xe(-x2)
2xe-x2
2xe^(-x²)
2xe to the power of (-x to the power of 2)
2xe^-x^2
2xe^(-x^2)dx
Similar expressions
2xe^(x^2)

Solving integrals/ 2xe^(-x^2)

Integral of 2xe^(-x^2) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |         2   
 |       -x    
 |  2*x*E    dx
 |             
/              
0

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

Integral((2*x)*E^(-x^2), (x, 0, 1))

Detail solution

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

Then let $du = - 2 x dx$ and substitute $- du$ :

$\int \left(- e^{u}\right)\, du$
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: $- e^{u}$
Now substitute $u$ back in:

$- e^{- x^{2}}$
Add the constant of integration:

$- e^{- x^{2}}+ \mathrm{constant}$

The answer is:

$- e^{- x^{2}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |        2             2
 |      -x            -x 
 | 2*x*E    dx = C - e   
 |                       
/

$$\int e^{- x^{2}} \cdot 2 x\, dx = C - e^{- x^{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     -1
1 - e

$$1 - e^{-1}$$

     -1
1 - e

$$1 - e^{-1}$$

1 - exp(-1)

Numerical answer [src]

0.632120558828558

0.632120558828558

The graph

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

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Identical expressions

Similar expressions

Integral of 2xe^(-x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution