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Canonical form:
2x^2-x+1
Graphing y =:
2x^2-x+1
Identical expressions
two x^2-x+ one
2x squared minus x plus 1
two x squared minus x plus one
2x2-x+1
2x²-x+1
2x to the power of 2-x+1
2x^2-x+1dx
Similar expressions
2x^2+x+1
2x^2-x-1

Integral of 2x^2-x+1 dx

The solution

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

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

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

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x^{2}\, dx = 2 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $\frac{2 x^{3}}{3}$
  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: $\frac{2 x^{3}}{3} - \frac{x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{2 x^{3}}{3} - \frac{x^{2}}{2} + x$
Now simplify:

$\frac{x \left(4 x^{2} - 3 x + 6\right)}{6}$
Add the constant of integration:

$\frac{x \left(4 x^{2} - 3 x + 6\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(4 x^{2} - 3 x + 6\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

25/6

$$\frac{25}{6}$$

25/6

$$\frac{25}{6}$$

25/6

Numerical answer [src]

4.16666666666667

4.16666666666667

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

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Integral of 2x^2-x+1 dx

Limits of integration:

The graph:

Piecewise:

The solution