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Graphing y =:
x^2-5x+2
Identical expressions
x^ two -5x+ two
x squared minus 5x plus 2
x to the power of two minus 5x plus two
x2-5x+2
x²-5x+2
x to the power of 2-5x+2
x^2-5x+2dx
Similar expressions
x^2-5x-2
x^2+5x+2

Integral of x^2-5x+2 dx

The solution

You have entered [src]

    2281                    
    ----                    
    500                     
      /                     
     |                      
     |     / 2          \   
     |     \x  - 5*x + 2/ dx
     |                      
    /                       
      ____                  
5   \/ 17                   
- - ------                  
2     2

$$\int\limits_{\frac{5}{2} - \frac{\sqrt{17}}{2}}^{\frac{2281}{500}} \left(\left(x^{2} - 5 x\right) + 2\right)\, dx$$

Integral(x^2 - 5*x + 2, (x, 5/2 - sqrt(17)/2, 2281/500))

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:
    
    $\int \left(- 5 x\right)\, dx = - 5 \int x\, dx$
    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: $- \frac{5 x^{2}}{2}$
  The result is: $\frac{x^{3}}{3} - \frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2\, dx = 2 x$
The result is: $\frac{x^{3}}{3} - \frac{5 x^{2}}{2} + 2 x$
Now simplify:

$\frac{x \left(2 x^{2} - 15 x + 12\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 15 x + 12\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 15 x + 12\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                  2    3
 | / 2          \                5*x    x 
 | \x  - 5*x + 2/ dx = C + 2*x - ---- + --
 |                                2     3 
/

$$\int \left(\left(x^{2} - 5 x\right) + 2\right)\, dx = C + \frac{x^{3}}{3} - \frac{5 x^{2}}{2} + 2 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                                    3                 2
                        /      ____\      /      ____\ 
                        |5   \/ 17 |      |5   \/ 17 | 
                        |- - ------|    5*|- - ------| 
  6096649709     ____   \2     2   /      \2     2   / 
- ---------- + \/ 17  - ------------- + ---------------
  375000000                   3                2

$$- \frac{6096649709}{375000000} - \frac{\left(\frac{5}{2} - \frac{\sqrt{17}}{2}\right)^{3}}{3} + \frac{5 \left(\frac{5}{2} - \frac{\sqrt{17}}{2}\right)^{2}}{2} + \sqrt{17}$$

                                    3                 2
                        /      ____\      /      ____\ 
                        |5   \/ 17 |      |5   \/ 17 | 
                        |- - ------|    5*|- - ------| 
  6096649709     ____   \2     2   /      \2     2   / 
- ---------- + \/ 17  - ------------- + ---------------
  375000000                   3                2

$$- \frac{6096649709}{375000000} - \frac{\left(\frac{5}{2} - \frac{\sqrt{17}}{2}\right)^{3}}{3} + \frac{5 \left(\frac{5}{2} - \frac{\sqrt{17}}{2}\right)^{2}}{2} + \sqrt{17}$$

-6096649709/375000000 + sqrt(17) - (5/2 - sqrt(17)/2)^3/3 + 5*(5/2 - sqrt(17)/2)^2/2

Numerical answer [src]

-11.682132193625

-11.682132193625

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

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Integral of x^2-5x+2 dx

Limits of integration:

The graph:

Piecewise:

The solution