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Identical expressions
two x^ three +4x^2-6x- eight
2x cubed plus 4x squared minus 6x minus 8
two x to the power of three plus 4x squared minus 6x minus eight
2x3+4x2-6x-8
2x³+4x²-6x-8
2x to the power of 3+4x to the power of 2-6x-8
2x^3+4x^2-6x-8dx
Similar expressions
2x^3-4x^2-6x-8
2x^3+4x^2+6x-8
2x^3+4x^2-6x+8

Solving integrals/ 2x^3+4x^2-6x-8

Integral of 2x^3+4x^2-6x-8 dx

The solution

You have entered [src]

  6                           
  /                           
 |                            
 |  /   3      2          \   
 |  \2*x  + 4*x  - 6*x - 8/ dx
 |                            
/                             
0

$$\int\limits_{0}^{6} \left(2 x^{3} + 4 x^{2} - 6 x - 8\right)\, dx$$

Integral(2*x^3 + 4*x^2 - 6*x - 1*8, (x, 0, 6))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 x^{3}\, dx = 2 \int x^{3}\, dx$
  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:
  
  $\int 4 x^{2}\, dx = 4 \int x^{2}\, dx$
  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: $\frac{4 x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 6 x\right)\, dx = - \int 6 x\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 6 x\, dx = 6 \int x\, dx$
    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: $3 x^{2}$
  So, the result is: $- 3 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(\left(-1\right) 8\right)\, dx = - 8 x$
The result is: $\frac{x^{4}}{2} + \frac{4 x^{3}}{3} - 3 x^{2} - 8 x$
Now simplify:

$\frac{x \left(3 x^{3} + 8 x^{2} - 18 x - 48\right)}{6}$
Add the constant of integration:

$\frac{x \left(3 x^{3} + 8 x^{2} - 18 x - 48\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(3 x^{3} + 8 x^{2} - 18 x - 48\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                       
 |                                   4                   3
 | /   3      2          \          x             2   4*x 
 | \2*x  + 4*x  - 6*x - 8/ dx = C + -- - 8*x - 3*x  + ----
 |                                  2                  3  
/

$${{x^4}\over{2}}+{{4\,x^3}\over{3}}-3\,x^2-8\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$780$$

Simplify

Numerical answer [src]

780.0

780.0

The graph

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

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Integral of 2x^3+4x^2-6x-8 dx

Limits of integration:

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Piecewise:

The solution