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

Integral of -x^3+x dx

The solution

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  2              
  /              
 |               
 |  /   3    \   
 |  \- x  + x/ dx
 |               
/                
0

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

Integral(-x^3 + x, (x, 0, 2))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-2

$$-2$$

-2

$$-2$$

-2

Numerical answer [src]

-2.0

-2.0

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

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Integral of -x^3+x dx

Limits of integration:

The graph:

Piecewise:

The solution