Mister Exam

Other calculators

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

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
  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 
 | 2*x*e    dx = C - e   
 |                       
/                        
$$\int 2 x e^{- x^{2}}\, dx = C - e^{- x^{2}}$$
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.