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Identical expressions
x^ four - two x^2-x- four
x to the power of 4 minus 2x squared minus x minus 4
x to the power of four minus two x squared minus x minus four
x4-2x2-x-4
x⁴-2x²-x-4
x to the power of 4-2x to the power of 2-x-4
x^4-2x^2-x-4dx
Similar expressions
x^4-2x^2-x+4
x^4+2x^2-x-4
x^4-2x^2+x-4

Solving integrals/ x^4-2x^2-x-4

Integral of x^4-2x^2-x-4 dx

The solution

You have entered [src]

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

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

Integral(x^4 - 2*x^2 - x - 1*4, (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:
  
  $\int \left(- 2 x^{2}\right)\, dx = - \int 2 x^{2}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x^{2}\, dx = 2 \int x^{2}\, dx$
    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: $\frac{2 x^{3}}{3}$
  So, the result is: $- \frac{2 x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x\right)\, dx = - \int x\, dx$
  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: $- \frac{x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(\left(-1\right) 4\right)\, dx = - 4 x$
The result is: $\frac{x^{5}}{5} - \frac{2 x^{3}}{3} - \frac{x^{2}}{2} - 4 x$
Now simplify:

$\frac{x \left(6 x^{4} - 20 x^{2} - 15 x - 120\right)}{30}$
Add the constant of integration:

$\frac{x \left(6 x^{4} - 20 x^{2} - 15 x - 120\right)}{30}+ \mathrm{constant}$

The answer is:

$\frac{x \left(6 x^{4} - 20 x^{2} - 15 x - 120\right)}{30}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{x^5}\over{5}}-{{2\,x^3}\over{3}}-{{x^2}\over{2}}-4\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-149 
-----
  30

$$-{{149}\over{30}}$$

-149 
-----
  30

$$- \frac{149}{30}$$

Упростить

Numerical answer [src]

-4.96666666666667

-4.96666666666667

The graph

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

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Similar expressions

Integral of x^4-2x^2-x-4 dx

Limits of integration:

The graph:

Piecewise:

The solution