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Similar expressions
2x*exp(x^2)

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

The solution

You have entered [src]

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

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

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

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   
 |                       
/

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

Simplify

The answer [src]

       2
     -x 
1 - e

$$1 - e^{- x^{2}}$$

       2
     -x 
1 - e

$$1 - e^{- x^{2}}$$

1 - exp(-x^2)

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution