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Identical expressions
(two x^2-x- one)
(2x squared minus x minus 1)
(two x squared minus x minus one)
(2x2-x-1)
2x2-x-1
(2x²-x-1)
(2x to the power of 2-x-1)
2x^2-x-1
(2x^2-x-1)dx
Similar expressions
(2x^2-x+1)
(2x^2+x-1)

Integral of (2x^2-x-1) dx

The solution

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  5                  
  /                  
 |                   
 |  /   2        \   
 |  \2*x  - x - 1/ dx
 |                   
/                    
2

$$\int\limits_{2}^{5} \left(\left(2 x^{2} - x\right) - 1\right)\, dx$$

Integral(2*x^2 - x - 1, (x, 2, 5))

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:
  
  $\int \left(-1\right)\, dx = - x$
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]

129/2

$$\frac{129}{2}$$

129/2

$$\frac{129}{2}$$

129/2

Numerical answer [src]

64.5

64.5

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