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Identical expressions
two x^ three -6x^2-4x
2x cubed minus 6x squared minus 4x
two x to the power of three minus 6x squared minus 4x
2x3-6x2-4x
2x³-6x²-4x
2x to the power of 3-6x to the power of 2-4x
2x^3-6x^2-4xdx
Similar expressions
2x^3+6x^2-4x
2x^3-6x^2+4x

Solving integrals/ 2x^3-6x^2-4x

Integral of 2x^3-6x^2-4x dx

The solution

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  1                       
  /                       
 |                        
 |  /   3      2      \   
 |  \2*x  - 6*x  - 4*x/ dx
 |                        
/                         
0

$$\int\limits_{0}^{1} \left(- 4 x + \left(2 x^{3} - 6 x^{2}\right)\right)\, dx$$

Integral(2*x^3 - 6*x^2 - 4*x, (x, 0, 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:
  
  $\int \left(- 4 x\right)\, dx = - 4 \int x\, dx$
  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: $- 2 x^{2}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x^{3}\, dx = 2 \int x^{3}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{3}\, dx = \frac{x^{4}}{4}$
    So, the result is: $\frac{x^{4}}{2}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 6 x^{2}\right)\, dx = - 6 \int x^{2}\, dx$
    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: $- 2 x^{3}$
  The result is: $\frac{x^{4}}{2} - 2 x^{3}$
The result is: $\frac{x^{4}}{2} - 2 x^{3} - 2 x^{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                             
 |                               4              
 | /   3      2      \          x       2      3
 | \2*x  - 6*x  - 4*x/ dx = C + -- - 2*x  - 2*x 
 |                              2               
/

$$\int \left(- 4 x + \left(2 x^{3} - 6 x^{2}\right)\right)\, dx = C + \frac{x^{4}}{2} - 2 x^{3} - 2 x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-7/2

$$- \frac{7}{2}$$

-7/2

$$- \frac{7}{2}$$

-7/2

Numerical answer [src]

-3.5

-3.5

The graph

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

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Integral of 2x^3-6x^2-4x dx

Limits of integration:

The graph:

Piecewise:

The solution