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

Solving integrals/ (2x^2-10x+8)

Integral of (2x^2-10x+8) dx

The solution

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

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

Simplify

Detail solution

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

$${{2\,x^3}\over{3}}-5\,x^2+8\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-9

$$-9$$

-9

$$-9$$

Simplify

Numerical answer [src]

-9.0

-9.0

The graph

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:

The graph:

Piecewise:

The solution