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Graphing y =:
x^3-2x^2+x
Derivative of:
x^3-2x^2+x
Identical expressions
x^ three - two x^2+x
x cubed minus 2x squared plus x
x to the power of three minus two x squared plus x
x3-2x2+x
x³-2x²+x
x to the power of 3-2x to the power of 2+x
x^3-2x^2+xdx
Similar expressions
x^3+2x^2+x
x^3-2x^2-x

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

The solution

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

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

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

Detail solution

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:
    
    $\int \left(- 2 x^{2}\right)\, dx = - 2 \int x^{2}\, dx$
    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: $- \frac{2 x^{3}}{3}$
  The result is: $\frac{x^{4}}{4} - \frac{2 x^{3}}{3}$
The result is: $\frac{x^{4}}{4} - \frac{2 x^{3}}{3} + \frac{x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(3 x^{2} - 8 x + 6\right)}{12}$
Add the constant of integration:

$\frac{x^{2} \left(3 x^{2} - 8 x + 6\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(3 x^{2} - 8 x + 6\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/12

$$\frac{1}{12}$$

1/12

$$\frac{1}{12}$$

1/12

Numerical answer [src]

0.0833333333333333

0.0833333333333333

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

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

Limits of integration:

The graph:

Piecewise:

The solution