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Graphing y =:
x^2-6x+10
Identical expressions
x^ two -6x+ ten
x squared minus 6x plus 10
x to the power of two minus 6x plus ten
x2-6x+10
x²-6x+10
x to the power of 2-6x+10
x^2-6x+10dx
Similar expressions
x^2-6x-10
x/(x^2-6*x+10)
x^2+6x+10

Integral of x^2-6x+10 dx

The solution

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  3                   
  /                   
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 |  / 2           \   
 |  \x  - 6*x + 10/ dx
 |                    
/                     
0

$$\int\limits_{0}^{3} \left(\left(x^{2} - 6 x\right) + 10\right)\, dx$$

Integral(x^2 - 6*x + 10, (x, 0, 3))

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:
  
  $\int 10\, dx = 10 x$
The result is: $\frac{x^{3}}{3} - 3 x^{2} + 10 x$
Now simplify:

$\frac{x \left(x^{2} - 9 x + 30\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 9 x + 30\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 9 x + 30\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                         3
 | / 2           \             2          x 
 | \x  - 6*x + 10/ dx = C - 3*x  + 10*x + --
 |                                        3 
/

$$\int \left(\left(x^{2} - 6 x\right) + 10\right)\, dx = C + \frac{x^{3}}{3} - 3 x^{2} + 10 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$12$$

Numerical answer [src]

12.0

12.0

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

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Integral of x^2-6x+10 dx

Limits of integration:

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Piecewise:

The solution