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Identical expressions
- two x^2-10x- eight
minus 2x squared minus 10x minus 8
minus two x squared minus 10x minus eight
-2x2-10x-8
-2x²-10x-8
-2x to the power of 2-10x-8
-2x^2-10x-8dx
Similar expressions
-2x^2-10x+8
2x^2-10x-8
-2x^2+10x-8

Integral of -2x^2-10x-8 dx

The solution

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 -1                       
  /                       
 |                        
 |  /     2           \   
 |  \- 2*x  - 10*x - 8/ dx
 |                        
/                         
-4

$$\int\limits_{-4}^{-1} \left(\left(- 2 x^{2} - 10 x\right) - 8\right)\, dx$$

Integral(-2*x^2 - 10*x - 8, (x, -4, -1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 2 x^{2}\right)\, dx = - 2 \int x^{2}\, dx$
    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: $- \frac{2 x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 10 x\right)\, dx = - 10 \int x\, dx$
    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: $- 5 x^{2}$
  The result is: $- \frac{2 x^{3}}{3} - 5 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-8\right)\, dx = - 8 x$
The result is: $- \frac{2 x^{3}}{3} - 5 x^{2} - 8 x$
Now simplify:

$- \frac{x \left(2 x^{2} + 15 x + 24\right)}{3}$
Add the constant of integration:

$- \frac{x \left(2 x^{2} + 15 x + 24\right)}{3}+ \mathrm{constant}$

The answer is:

$- \frac{x \left(2 x^{2} + 15 x + 24\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                                              3
 | /     2           \                   2   2*x 
 | \- 2*x  - 10*x - 8/ dx = C - 8*x - 5*x  - ----
 |                                            3  
/

$$\int \left(\left(- 2 x^{2} - 10 x\right) - 8\right)\, dx = C - \frac{2 x^{3}}{3} - 5 x^{2} - 8 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$9$$

Numerical answer [src]

9.0

9.0

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

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Integral of -2x^2-10x-8 dx

Limits of integration:

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Piecewise:

The solution