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Identical expressions
-x^(two)-4x
minus x to the power of (2) minus 4x
minus x to the power of (two) minus 4x
-x(2)-4x
-x2-4x
-x^2-4x
-x^(2)-4xdx
Similar expressions
-x^(2)+4x
x^(2)-4x

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

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

The solution

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

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

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

Detail solution

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

$\frac{x^{2} \left(- x - 6\right)}{3}$
Add the constant of integration:

$\frac{x^{2} \left(- x - 6\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(- x - 6\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

22/3

$${{22}\over{3}}$$

22/3

$$\frac{22}{3}$$

Упростить

Numerical answer [src]

7.33333333333333

7.33333333333333

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution