Mister Exam

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Integral of d{x}:
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Integral of atan(x)
Integral of cosnx
Integral of 1/(sqrt(1-x^2))
Factor squared:
2*x^2-x+2
Factor polynomial:
2*x^2-x+2
Identical expressions
two *x^ two -x+ two
2 multiply by x squared minus x plus 2
two multiply by x to the power of two minus x plus two
2*x2-x+2
2*x²-x+2
2*x to the power of 2-x+2
2x^2-x+2
2x2-x+2
2*x^2-x+2dx
Similar expressions
2*x^2-x-2
2*x^2+x+2

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

The solution

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

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

Integral(2*x^2 - x + 2, (x, 0, 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:
  
  $\int 2\, dx = 2 x$
The result is: $\frac{2 x^{3}}{3} - \frac{x^{2}}{2} + 2 x$
Now simplify:

$\frac{x \left(4 x^{2} - 3 x + 12\right)}{6}$
Add the constant of integration:

$\frac{x \left(4 x^{2} - 3 x + 12\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(4 x^{2} - 3 x + 12\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

22/3

$$\frac{22}{3}$$

22/3

$$\frac{22}{3}$$

22/3

Numerical answer [src]

7.33333333333333

7.33333333333333

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

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

Limits of integration:

The graph:

Piecewise:

The solution