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Identical expressions
(x/ two)*(x- three)
(x divide by 2) multiply by (x minus 3)
(x divide by two) multiply by (x minus three)
(x/2)(x-3)
x/2x-3
(x divide by 2)*(x-3)
(x/2)*(x-3)dx
Similar expressions
(x/2)*(x+3)
(dx)/((2x-3)^5)

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

The solution

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  5             
  /             
 |              
 |  x           
 |  -*(x - 3) dx
 |  2           
 |              
/               
3

$$\int\limits_{3}^{5} \frac{x}{2} \left(x - 3\right)\, dx$$

Integral((x/2)*(x - 3), (x, 3, 5))

Detail solution

Rewrite the integrand:

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

$\frac{x^{2} \left(2 x - 9\right)}{12}$
Add the constant of integration:

$\frac{x^{2} \left(2 x - 9\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 x - 9\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                       2    3
 | x                  3*x    x 
 | -*(x - 3) dx = C - ---- + --
 | 2                   4     6 
 |                             
/

$$\int \frac{x}{2} \left(x - 3\right)\, dx = C + \frac{x^{3}}{6} - \frac{3 x^{2}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

13/3

$$\frac{13}{3}$$

13/3

$$\frac{13}{3}$$

13/3

Numerical answer [src]

4.33333333333333

4.33333333333333

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

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

Limits of integration:

The graph:

Piecewise:

The solution