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Identical expressions
(x^ four -x^ three -x^ two)
(x to the power of 4 minus x cubed minus x squared )
(x to the power of four minus x to the power of three minus x to the power of two)
(x4-x3-x2)
x4-x3-x2
(x⁴-x³-x²)
(x to the power of 4-x to the power of 3-x to the power of 2)
x^4-x^3-x^2
(x^4-x^3-x^2)dx
Similar expressions
(x^4-x^3+x^2)
(x^4+x^3-x^2)

Solving integrals/ (x^4-x^3-x^2)

Integral of (x^4-x^3-x^2) dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |  / 4    3    2\   
 |  \x  - x  - x / dx
 |                   
/                    
0

$$\int\limits_{0}^{1} \left(x^{4} - x^{3} - x^{2}\right)\, dx$$

Integral(x^4 - x^3 - x^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{4}\, dx = \frac{x^{5}}{5}$
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 a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
  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: $- \frac{x^{3}}{3}$
The result is: $\frac{x^{5}}{5} - \frac{x^{4}}{4} - \frac{x^{3}}{3}$
Now simplify:

$\frac{x^{3} \cdot \left(12 x^{2} - 15 x - 20\right)}{60}$
Add the constant of integration:

$\frac{x^{3} \cdot \left(12 x^{2} - 15 x - 20\right)}{60}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \cdot \left(12 x^{2} - 15 x - 20\right)}{60}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                          3    4    5
 | / 4    3    2\          x    x    x 
 | \x  - x  - x / dx = C - -- - -- + --
 |                         3    4    5 
/

$${{x^5}\over{5}}-{{x^4}\over{4}}-{{x^3}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-23 
----
 60

$$-{{23}\over{60}}$$

-23 
----
 60

$$- \frac{23}{60}$$

Simplify

Numerical answer [src]

-0.383333333333333

-0.383333333333333

The graph

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

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Integral of (x^4-x^3-x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution