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Integral of d{x}:
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Graphing y =:
2x^2-8x+6
Identical expressions
two x^2-8x+ six
2x squared minus 8x plus 6
two x squared minus 8x plus six
2x2-8x+6
2x²-8x+6
2x to the power of 2-8x+6
2x^2-8x+6dx
Similar expressions
2x^2+8x+6
2x^2-8x-6

Integral of 2x^2-8x+6 dx

The solution

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  1                    
  /                    
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 |  /   2          \   
 |  \2*x  - 8*x + 6/ dx
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/                      
3

$$\int\limits_{3}^{1} \left(\left(2 x^{2} - 8 x\right) + 6\right)\, dx$$

Integral(2*x^2 - 8*x + 6, (x, 3, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x^{2}\, dx = 2 \int x^{2}\, dx$
    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: $\frac{2 x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 8 x\right)\, dx = - 8 \int x\, dx$
    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: $- 4 x^{2}$
  The result is: $\frac{2 x^{3}}{3} - 4 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 6\, dx = 6 x$
The result is: $\frac{2 x^{3}}{3} - 4 x^{2} + 6 x$
Now simplify:

$\frac{2 x \left(x^{2} - 6 x + 9\right)}{3}$
Add the constant of integration:

$\frac{2 x \left(x^{2} - 6 x + 9\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{2 x \left(x^{2} - 6 x + 9\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                           3
 | /   2          \             2         2*x 
 | \2*x  - 8*x + 6/ dx = C - 4*x  + 6*x + ----
 |                                         3  
/

$$\int \left(\left(2 x^{2} - 8 x\right) + 6\right)\, dx = C + \frac{2 x^{3}}{3} - 4 x^{2} + 6 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

8/3

$$\frac{8}{3}$$

8/3

$$\frac{8}{3}$$

8/3

Numerical answer [src]

2.66666666666667

2.66666666666667

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

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Integral of 2x^2-8x+6 dx

Limits of integration:

The graph:

Piecewise:

The solution