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Identical expressions
(two x^2-4x+ five)dx
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Similar expressions
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(2x^2-4x-5)dx

Integral of (2x^2-4x+5)dx dx

The solution

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  2                    
  /                    
 |                     
 |  /   2          \   
 |  \2*x  - 4*x + 5/ dx
 |                     
/                      
-1

$$\int\limits_{-1}^{2} \left(\left(2 x^{2} - 4 x\right) + 5\right)\, dx$$

Integral(2*x^2 - 4*x + 5, (x, -1, 2))

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:
    
    $\int 2 x^{2}\, dx = 2 \int x^{2}\, dx$
    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:
    
    $\int \left(- 4 x\right)\, dx = - 4 \int x\, dx$
    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: $- 2 x^{2}$
  The result is: $\frac{2 x^{3}}{3} - 2 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 5\, dx = 5 x$
The result is: $\frac{2 x^{3}}{3} - 2 x^{2} + 5 x$
Now simplify:

$\frac{x \left(2 x^{2} - 6 x + 15\right)}{3}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 6 x + 15\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 6 x + 15\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                           3
 | /   2          \             2         2*x 
 | \2*x  - 4*x + 5/ dx = C - 2*x  + 5*x + ----
 |                                         3  
/

$$\int \left(\left(2 x^{2} - 4 x\right) + 5\right)\, dx = C + \frac{2 x^{3}}{3} - 2 x^{2} + 5 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$15$$

Numerical answer [src]

15.0

15.0

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

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Integral of (2x^2-4x+5)dx dx

Limits of integration:

The graph:

Piecewise:

The solution