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Solving integrals/ x^3+x^2-2x

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

The solution

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

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

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

$x^{2} \left(\frac{x^{2}}{4} + \frac{x}{3} - 1\right)$
Add the constant of integration:

$x^{2} \left(\frac{x^{2}}{4} + \frac{x}{3} - 1\right)+ \mathrm{constant}$

The answer is:

$x^{2} \left(\frac{x^{2}}{4} + \frac{x}{3} - 1\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{x^4}\over{4}}+{{x^3}\over{3}}-x^2$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-5/12

$$-{{5}\over{12}}$$

-5/12

$$- \frac{5}{12}$$

Упростить

Numerical answer [src]

-0.416666666666667

-0.416666666666667

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution