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Factor polynomial:
x^3-x+2
Graphing y =:
x^3-x+2
Derivative of:
x^3-x+2
Identical expressions
x^ three -x+ two
x cubed minus x plus 2
x to the power of three minus x plus two
x3-x+2
x³-x+2
x to the power of 3-x+2
x^3-x+2dx
Similar expressions
x^3-x-2
x^3+x+2

Solving integrals/ x^3-x+2

Integral of x^3-x+2 dx

The solution

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  1                
  /                
 |                 
 |  / 3        \   
 |  \x  - x + 2/ dx
 |                 
/                  
0

$$\int\limits_{0}^{1} \left(\left(x^{3} - x\right) + 2\right)\, dx$$

Integral(x^3 - x + 2, (x, 0, 1))

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

$\frac{x \left(x^{3} - 2 x + 8\right)}{4}$
Add the constant of integration:

$\frac{x \left(x^{3} - 2 x + 8\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} - 2 x + 8\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

7/4

$$\frac{7}{4}$$

7/4

$$\frac{7}{4}$$

7/4

Numerical answer [src]

1.75

1.75

The graph

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

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Identical expressions

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Integral of x^3-x+2 dx

Limits of integration:

The graph:

Piecewise:

The solution