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Derivative of:
x^2-x+1
Graphing y =:
x^2-x+1
Factor polynomial:
x^2-x+1
Identical expressions
x^ two -x+ one
x squared minus x plus 1
x to the power of two minus x plus one
x2-x+1
x²-x+1
x to the power of 2-x+1
x^2-x+1dx
Similar expressions
x^2+x+1
x^2-x-1
(x^2-x+1)*sin4x

Integral of x^2-x+1 dx

The solution

You have entered [src]

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

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

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

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

$x \left(\frac{x^{2}}{3} - \frac{x}{2} + 1\right)$
Add the constant of integration:

$x \left(\frac{x^{2}}{3} - \frac{x}{2} + 1\right)+ \mathrm{constant}$

The answer is:

$x \left(\frac{x^{2}}{3} - \frac{x}{2} + 1\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                            2    3
 | / 2        \              x    x 
 | \x  - x + 1/ dx = C + x - -- + --
 |                           2    3 
/

$$\int \left(\left(x^{2} - x\right) + 1\right)\, dx = C + \frac{x^{3}}{3} - \frac{x^{2}}{2} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

11/6

$$\frac{11}{6}$$

11/6

$$\frac{11}{6}$$

11/6

Numerical answer [src]

1.83333333333333

1.83333333333333

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

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Identical expressions

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Integral of x^2-x+1 dx

Limits of integration:

The graph:

Piecewise:

The solution