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Identical expressions
-x^ two + eight + two *x
minus x squared plus 8 plus 2 multiply by x
minus x to the power of two plus eight plus two multiply by x
-x2+8+2*x
-x²+8+2*x
-x to the power of 2+8+2*x
-x^2+8+2x
-x2+8+2x
-x^2+8+2*xdx
Similar expressions
-x^2-8+2*x
x^2+8+2*x
-x^2+8-2*x

Integral of -x^2+8+2*x dx

The solution

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  4                    
  /                    
 |                     
 |  /   2          \   
 |  \- x  + 8 + 2*x/ dx
 |                     
/                      
-2

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

Integral(-x^2 + 8 + 2*x, (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:
  
  $\int 2 x\, dx = 2 \int x\, dx$
  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: $x^{2}$
1. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 8\, dx = 8 x$
  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: $- \frac{x^{3}}{3}$
  The result is: $- \frac{x^{3}}{3} + 8 x$
The result is: $- \frac{x^{3}}{3} + x^{2} + 8 x$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

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Plot the graph f(x)

The answer [src]

$$36$$

Numerical answer [src]

36.0

36.0

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

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Integral of -x^2+8+2*x dx

Limits of integration:

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Piecewise:

The solution