Integral of (x²-6x+8)dx dx

The solution

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

Integral(x^2 - 6*x + 8, (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:
  
  $\int 8\, dx = 8 x$
The result is: $\frac{x^{3}}{3} - 3 x^{2} + 8 x$
Now simplify:

$\frac{x \left(x^{2} - 9 x + 24\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 9 x + 24\right)}{3}+ \mathrm{constant}$

The answer is:

\frac{x \left(x^{2} - 9 x + 24\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

4/3

\frac{4}{3}

4/3

\frac{4}{3}

4/3

Numerical answer [src]

1.33333333333333

1.33333333333333

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

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Integral of (x²-6x+8)dx dx

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