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Identical expressions
xe-x^ two
xe minus x squared
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xe-x²
xe-x to the power of 2
xe-x^2dx
Similar expressions
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Solving integrals/ xe-x^2

Integral of xe-x^2 dx

The solution

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

$$\int\limits_{0}^{1} \left(- x^{2} + e x\right)\, dx$$

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $- \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int e x\, dx = e \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{e x^{2}}{2}$
The result is: $- \frac{x^{3}}{3} + \frac{e x^{2}}{2}$
Now simplify:

$x^{2} \left(- \frac{x}{3} + \frac{e}{2}\right)$
Add the constant of integration:

$x^{2} \left(- \frac{x}{3} + \frac{e}{2}\right)+ \mathrm{constant}$

The answer is:

$x^{2} \left(- \frac{x}{3} + \frac{e}{2}\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                      3      2
 | /       2\          x    E*x 
 | \x*E - x / dx = C - -- + ----
 |                     3     2  
/

$$\int \left(- x^{2} + e x\right)\, dx = C - \frac{x^{3}}{3} + \frac{e x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1   E
- - + -
  3   2

$$- \frac{1}{3} + \frac{e}{2}$$

  1   E
- - + -
  3   2

$$- \frac{1}{3} + \frac{e}{2}$$

-1/3 + E/2

Numerical answer [src]

1.02580758089619

1.02580758089619

The graph

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

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Integral of xe-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution