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Integral of d{x}:
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Integral of √(1-x^2)
Integral of 1/(2x)
Integral of (e^x)/x
Identical expressions
x^ three *(x- two)
x cubed multiply by (x minus 2)
x to the power of three multiply by (x minus two)
x3*(x-2)
x3*x-2
x³*(x-2)
x to the power of 3*(x-2)
x^3(x-2)
x3(x-2)
x3x-2
x^3x-2
x^3*(x-2)dx
Similar expressions
x^3*(x+2)

Integral of x^3*(x-2) dx

The solution

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  3              
  /              
 |               
 |   3           
 |  x *(x - 2) dx
 |               
/                
2

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

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

Detail solution

Rewrite the integrand:

$x^{3} \left(x - 2\right) = x^{4} - 2 x^{3}$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{4}\, dx = \frac{x^{5}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x^{3}\right)\, dx = - 2 \int x^{3}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{3}\, dx = \frac{x^{4}}{4}$
  So, the result is: $- \frac{x^{4}}{2}$
The result is: $\frac{x^{5}}{5} - \frac{x^{4}}{2}$
Now simplify:

$\frac{x^{4} \left(2 x - 5\right)}{10}$
Add the constant of integration:

$\frac{x^{4} \left(2 x - 5\right)}{10}+ \mathrm{constant}$

The answer is:

$\frac{x^{4} \left(2 x - 5\right)}{10}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                      4    5
 |  3                  x    x 
 | x *(x - 2) dx = C - -- + --
 |                     2    5 
/

$$\int x^{3} \left(x - 2\right)\, dx = C + \frac{x^{5}}{5} - \frac{x^{4}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

97
--
10

$$\frac{97}{10}$$

97
--
10

$$\frac{97}{10}$$

97/10

Numerical answer [src]

9.7

9.7

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

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Integral of x^3*(x-2) dx

Limits of integration:

The graph:

Piecewise:

The solution