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Integral of d{x}:
Integral of e^(-x)
Integral of -sin(x)
Integral of cos(x/2)
Integral of x-2
Canonical form:
3x^2-x-2
Identical expressions
3x^ two -x- two
3x squared minus x minus 2
3x to the power of two minus x minus two
3x2-x-2
3x²-x-2
3x to the power of 2-x-2
3x^2-x-2dx
Similar expressions
3x^2+x-2
3x^2-x+2

Integral of 3x^2-x-2 dx

The solution

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  1                  
  /                  
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 |  /   2        \   
 |  \3*x  - x - 2/ dx
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/                    
0

$$\int\limits_{0}^{1} \left(\left(3 x^{2} - x\right) - 2\right)\, dx$$

Integral(3*x^2 - x - 2, (x, 0, 1))

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-3/2

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

-3/2

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

-3/2

Numerical answer [src]

-1.5

-1.5

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

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Integral of 3x^2-x-2 dx

Limits of integration:

The graph:

Piecewise:

The solution