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Identical expressions
- four x^4-x^ five
minus 4x to the power of 4 minus x to the power of 5
minus four x to the power of 4 minus x to the power of five
-4x4-x5
-4x⁴-x⁵
-4x^4-x^5dx
Similar expressions
-4x^4+x^5
4x^4-x^5

Solving integrals/ -4x^4-x^5

Integral of -4x^4-x^5 dx

The solution

You have entered [src]

  4                 
  /                 
 |                  
 |  /     4    5\   
 |  \- 4*x  - x / dx
 |                  
/                   
-2

$$\int\limits_{-2}^{4} \left(- x^{5} - 4 x^{4}\right)\, dx$$

Integral(-4*x^4 - x^5, (x, -2, 4))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x^{5}\right)\, dx = - \int x^{5}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{5}\, dx = \frac{x^{6}}{6}$
  So, the result is: $- \frac{x^{6}}{6}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 x^{4}\right)\, dx = - 4 \int x^{4}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{4}\, dx = \frac{x^{5}}{5}$
  So, the result is: $- \frac{4 x^{5}}{5}$
The result is: $- \frac{x^{6}}{6} - \frac{4 x^{5}}{5}$
Now simplify:

$\frac{x^{5} \left(- 5 x - 24\right)}{30}$
Add the constant of integration:

$\frac{x^{5} \left(- 5 x - 24\right)}{30}+ \mathrm{constant}$

The answer is:

$\frac{x^{5} \left(- 5 x - 24\right)}{30}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                           5    6
 | /     4    5\          4*x    x 
 | \- 4*x  - x / dx = C - ---- - --
 |                         5     6 
/

$$-{{x^6}\over{6}}-{{4\,x^5}\over{5}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-7584/5

$$-{{7584}\over{5}}$$

-7584/5

$$- \frac{7584}{5}$$

Упростить

Numerical answer [src]

-1516.8

-1516.8

The graph

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

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Integral of -4x^4-x^5 dx

Limits of integration:

The graph:

Piecewise:

The solution