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Identical expressions
x^ four -(two /2x)- four
x to the power of 4 minus (2 divide by 2x) minus 4
x to the power of four minus (two divide by 2x) minus four
x4-(2/2x)-4
x4-2/2x-4
x⁴-(2/2x)-4
x^4-2/2x-4
x^4-(2 divide by 2x)-4
x^4-(2/2x)-4dx
Similar expressions
x^4+(2/2x)-4
x^4-(2/2x)+4

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

The solution

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

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

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

$\frac{x \left(2 x^{4} - 5 x - 40\right)}{10}$
Add the constant of integration:

$\frac{x \left(2 x^{4} - 5 x - 40\right)}{10}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{4} - 5 x - 40\right)}{10}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \left(\left(x^{4} - x\right) - 4\right)\, dx = C + \frac{x^{5}}{5} - \frac{x^{2}}{2} - 4 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-43 
----
 10

$$- \frac{43}{10}$$

-43 
----
 10

$$- \frac{43}{10}$$

-43/10

Numerical answer [src]

-4.3

-4.3

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

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

Limits of integration:

The graph:

Piecewise:

The solution