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Identical expressions
(x^ two -6x+ nine)dx
(x squared minus 6x plus 9)dx
(x to the power of two minus 6x plus nine)dx
(x2-6x+9)dx
x2-6x+9dx
(x²-6x+9)dx
(x to the power of 2-6x+9)dx
x^2-6x+9dx
Similar expressions
(x^2+6x+9)dx
(x^2-6x-9)dx

Solving integrals/ (x^2-6x+9)dx

Integral of (x^2-6x+9)dx dx

The solution

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  2                  
  /                  
 |                   
 |  / 2          \   
 |  \x  - 6*x + 9/ dx
 |                   
/                    
-1

$$\int\limits_{-1}^{2} \left(\left(x^{2} - 6 x\right) + 9\right)\, dx$$

Integral(x^2 - 6*x + 9, (x, -1, 2))

Detail solution

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

$\frac{x \left(x^{2} - 9 x + 27\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 9 x + 27\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 9 x + 27\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                       3
 | / 2          \             2         x 
 | \x  - 6*x + 9/ dx = C - 3*x  + 9*x + --
 |                                      3 
/

$$\int \left(\left(x^{2} - 6 x\right) + 9\right)\, dx = C + \frac{x^{3}}{3} - 3 x^{2} + 9 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$21$$

Numerical answer [src]

21.0

21.0

The graph

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

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Integral of (x^2-6x+9)dx dx

Limits of integration:

The graph:

Piecewise:

The solution