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Graphing y =:
x^3-3x+1
Identical expressions
x^ three -3x+ one
x cubed minus 3x plus 1
x to the power of three minus 3x plus one
x3-3x+1
x³-3x+1
x to the power of 3-3x+1
x^3-3x+1dx
Similar expressions
x^3+3x+1
x^3-3x-1

Integral of x^3-3x+1 dx

The solution

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

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

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

Detail solution

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

$\frac{x \left(x^{3} - 6 x + 4\right)}{4}$
Add the constant of integration:

$\frac{x \left(x^{3} - 6 x + 4\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} - 6 x + 4\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                2    4
 | / 3          \              3*x    x 
 | \x  - 3*x + 1/ dx = C + x - ---- + --
 |                              2     4 
/

$$\int \left(\left(x^{3} - 3 x\right) + 1\right)\, dx = C + \frac{x^{4}}{4} - \frac{3 x^{2}}{2} + x$$

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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Integral of x^3-3x+1 dx

Limits of integration:

The graph:

Piecewise:

The solution