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

Solving integrals/ x^2-2x-1

Integral of x^2-2x-1 dx

The solution

You have entered [src]

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

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-5/3

$$- \frac{5}{3}$$

-5/3

$$- \frac{5}{3}$$

-5/3

Numerical answer [src]

-1.66666666666667

-1.66666666666667

The graph

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

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Identical expressions

Similar expressions

Integral of x^2-2x-1 dx

Limits of integration:

The graph:

Piecewise:

The solution