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Integral of d{x}:
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Integral of 1/(x)
Identical expressions
- two x^2+8x- six
minus 2x squared plus 8x minus 6
minus two x squared plus 8x minus 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
-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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0

$$\int\limits_{0}^{1} \left(\left(- 2 x^{2} + 8 x\right) - 6\right)\, dx$$

Integral(-2*x^2 + 8*x - 6, (x, 0, 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:
    
    $\int \left(- 2 x^{2}\right)\, dx = - 2 \int x^{2}\, dx$
    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:
    
    $\int 8 x\, dx = 8 \int x\, dx$
    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:
  
  $\int \left(-6\right)\, dx = - 6 x$
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 - 6*x + 4*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