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Graphing y =:
3x^3-x
Identical expressions
three x^3-x
3x cubed minus x
three x cubed minus x
3x3-x
3x³-x
3x to the power of 3-x
3x^3-xdx
Similar expressions
3x^3+x

Integral of 3x^3-x dx

The solution

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

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

Integral(3*x^3 - 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:
  
  $\int 3 x^{3}\, dx = 3 \int x^{3}\, dx$
  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: $\frac{3 x^{4}}{4}$
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: $\frac{3 x^{4}}{4} - \frac{x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(3 x^{2} - 2\right)}{4}$
Add the constant of integration:

$\frac{x^{2} \left(3 x^{2} - 2\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(3 x^{2} - 2\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/4

$$\frac{1}{4}$$

1/4

$$\frac{1}{4}$$

1/4

Numerical answer [src]

0.25

0.25

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

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Identical expressions

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Integral of 3x^3-x dx

Limits of integration:

The graph:

Piecewise:

The solution