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Identical expressions
-(two x^2-x- one)
minus (2x squared minus x minus 1)
minus (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)
-(2x^2+x-1)

Solving integrals/ -(2x^2-x-1)

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

The solution

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

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

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

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x^{2}\right)\, dx = - 2 \int x^{2}\, dx$
  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 $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
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 
 | \1 + x - 2*x / dx = C + x + -- - ----
 |                             2     3  
/

$$-{{2\,x^3}\over{3}}+{{x^2}\over{2}}+x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2/3

$$-{{2}\over{3}}$$

-2/3

$$- \frac{2}{3}$$

Упростить

Numerical answer [src]

-0.666666666666667

-0.666666666666667

The graph

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