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Identical expressions
x^ three -6x^ two +x- one
x cubed minus 6x squared plus x minus 1
x to the power of three minus 6x to the power of two plus x minus one
x3-6x2+x-1
x³-6x²+x-1
x to the power of 3-6x to the power of 2+x-1
x^3-6x^2+x-1dx
Similar expressions
x^3-6x^2+x+1
x^3+6x^2+x-1
x^3-6x^2-x-1

Integral of x^3-6x^2+x-1 dx

The solution

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

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

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

$\frac{x \left(x^{3} - 8 x^{2} + 2 x - 4\right)}{4}$
Add the constant of integration:

$\frac{x \left(x^{3} - 8 x^{2} + 2 x - 4\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} - 8 x^{2} + 2 x - 4\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                               2               4
 | / 3      2        \          x           3   x 
 | \x  - 6*x  + x - 1/ dx = C + -- - x - 2*x  + --
 |                              2               4 
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-9/4

$$- \frac{9}{4}$$

-9/4

$$- \frac{9}{4}$$

-9/4

Numerical answer [src]

-2.25

-2.25

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

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Integral of x^3-6x^2+x-1 dx

Limits of integration:

The graph:

Piecewise:

The solution