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Integral of d{x}:
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Identical expressions
x(x- three)²
x(x minus 3)²
x(x minus three)²
xx-3²
x(x-3)²dx
Similar expressions
x(x+3)²

Solving integrals/ x(x-3)²

Integral of x(x-3)² dx

The solution

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  1              
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 |           2   
 |  x*(x - 3)  dx
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0

$$\int\limits_{0}^{1} x \left(x - 3\right)^{2}\, dx$$

Integral(x*(x - 3)^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

$x \left(x - 3\right)^{2} = x^{3} - 6 x^{2} + 9 x$
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:
  
  $\int \left(- 6 x^{2}\right)\, dx = - 6 \int x^{2}\, dx$
  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: $- 2 x^{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 9 x\, dx = 9 \int x\, dx$
  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: $\frac{9 x^{2}}{2}$
The result is: $\frac{x^{4}}{4} - 2 x^{3} + \frac{9 x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(x^{2} - 8 x + 18\right)}{4}$
Add the constant of integration:

$\frac{x^{2} \left(x^{2} - 8 x + 18\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(x^{2} - 8 x + 18\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                             4      2
 |          2             3   x    9*x 
 | x*(x - 3)  dx = C - 2*x  + -- + ----
 |                            4     2  
/

$$\int x \left(x - 3\right)^{2}\, dx = C + \frac{x^{4}}{4} - 2 x^{3} + \frac{9 x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

11/4

$$\frac{11}{4}$$

11/4

$$\frac{11}{4}$$

11/4

Numerical answer [src]

2.75

2.75

The graph

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

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Integral of x(x-3)² dx

Limits of integration:

The graph:

Piecewise:

The solution