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Integral of d{x}:
Integral of dx/(1+x^2)
Integral of exp(y)
Integral of -exp(-x)
Integral of ln(x)/√x
Graphing y =:
x(x-2)^2
Identical expressions
x(x- two)^ two
x(x minus 2) squared
x(x minus two) to the power of two
x(x-2)2
xx-22
x(x-2)²
x(x-2) to the power of 2
xx-2^2
x(x-2)^2dx
Similar expressions
x(x+2)^2

Solving integrals/ x(x-2)^2

Integral of x(x-2)^2 dx

The solution

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  2              
  /              
 |               
 |           2   
 |  x*(x - 2)  dx
 |               
/                
0

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

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

Detail solution

Rewrite the integrand:

$x \left(x - 2\right)^{2} = x^{3} - 4 x^{2} + 4 x$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 x^{2}\right)\, dx = - 4 \int x^{2}\, dx$
  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: $- \frac{4 x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 x\, dx = 4 \int x\, dx$
  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: $2 x^{2}$
The result is: $\frac{x^{4}}{4} - \frac{4 x^{3}}{3} + 2 x^{2}$
Now simplify:

$\frac{x^{2} \left(3 x^{2} - 16 x + 24\right)}{12}$
Add the constant of integration:

$\frac{x^{2} \left(3 x^{2} - 16 x + 24\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(3 x^{2} - 16 x + 24\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                               3    4
 |          2             2   4*x    x 
 | x*(x - 2)  dx = C + 2*x  - ---- + --
 |                             3     4 
/

$$\int x \left(x - 2\right)^{2}\, dx = C + \frac{x^{4}}{4} - \frac{4 x^{3}}{3} + 2 x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

4/3

$$\frac{4}{3}$$

4/3

$$\frac{4}{3}$$

4/3

Numerical answer [src]

1.33333333333333

1.33333333333333

The graph

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

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Integral of x(x-2)^2 dx

Limits of integration:

The graph:

Piecewise:

The solution