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Integral of d{x}:
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Integral of x^y
Factor squared:
x^2-2*x+2
Factor polynomial:
x^2-2*x+2
Identical expressions
x^ two - two *x+ two
x squared minus 2 multiply by x plus 2
x to the power of two minus two multiply by x plus two
x2-2*x+2
x²-2*x+2
x to the power of 2-2*x+2
x^2-2x+2
x2-2x+2
x^2-2*x+2dx
Similar expressions
x^2+2*x+2
x^2-2*x-2

Solving integrals/ x^2-2*x+2

Integral of x^2-2*x+2 dx

The solution

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  1                  
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 |  / 2          \   
 |  \x  - 2*x + 2/ dx
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0

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

Integral(x^2 - 2*x + 2, (x, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$${{x^3}\over{3}}-x^2+2\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

4/3

$${{4}\over{3}}$$

4/3

$$\frac{4}{3}$$

Упростить

Numerical answer [src]

1.33333333333333

1.33333333333333

The graph

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

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Identical expressions

Similar expressions

Integral of x^2-2*x+2 dx

Limits of integration:

The graph:

Piecewise:

The solution