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How to use it?
Integral of d{x}:
Integral of cos2xsinx
Integral of (-1)^x
Integral of (x^5+x^4-8)/(x^3-4x)
Integral of (x^3-1)/(x+3)
Identical expressions
xe(x^ two)
xe(x squared )
xe(x to the power of two)
xe(x2)
xex2
xe(x²)
xe(x to the power of 2)
xex^2
xe(x^2)dx

Solving integrals/ xe(x^2)

Integral of xe(x^2) dx

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = x^{2}$ .

Then let $du = 2 x dx$ and substitute $\frac{e du}{2}$ :

$\int \frac{e u}{2}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int u\, du = \frac{e \int u\, du}{2}$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u\, du = \frac{u^{2}}{2}$
  So, the result is: $\frac{u^{2} e}{4}$
Now substitute $u$ back in:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

E
-
4

$$\frac{e}{4}$$

=

E
-
4

$$\frac{e}{4}$$

E/4

Numerical answer [src]

0.679570457114761

0.679570457114761

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