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Identical expressions
two x^2-5x+ seven
2x squared minus 5x plus 7
two x squared minus 5x plus seven
2x2-5x+7
2x²-5x+7
2x to the power of 2-5x+7
2x^2-5x+7dx
Similar expressions
2x^2+5x+7
2x^2-5x-7

Integral of 2x^2-5x+7 dx

The solution

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  1                    
  /                    
 |                     
 |  /   2          \   
 |  \2*x  - 5*x + 7/ dx
 |                     
/                      
0

$$\int\limits_{0}^{1} \left(\left(2 x^{2} - 5 x\right) + 7\right)\, dx$$

Integral(2*x^2 - 5*x + 7, (x, 0, 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:
    
    $\int 2 x^{2}\, dx = 2 \int x^{2}\, dx$
    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:
    
    $\int \left(- 5 x\right)\, dx = - 5 \int x\, dx$
    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: $- \frac{5 x^{2}}{2}$
  The result is: $\frac{2 x^{3}}{3} - \frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 7\, dx = 7 x$
The result is: $\frac{2 x^{3}}{3} - \frac{5 x^{2}}{2} + 7 x$
Now simplify:

$\frac{x \left(4 x^{2} - 15 x + 42\right)}{6}$
Add the constant of integration:

$\frac{x \left(4 x^{2} - 15 x + 42\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(4 x^{2} - 15 x + 42\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                    2      3
 | /   2          \                5*x    2*x 
 | \2*x  - 5*x + 7/ dx = C + 7*x - ---- + ----
 |                                  2      3  
/

$$\int \left(\left(2 x^{2} - 5 x\right) + 7\right)\, dx = C + \frac{2 x^{3}}{3} - \frac{5 x^{2}}{2} + 7 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

31/6

$$\frac{31}{6}$$

31/6

$$\frac{31}{6}$$

31/6

Numerical answer [src]

5.16666666666667

5.16666666666667

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

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Integral of 2x^2-5x+7 dx

Limits of integration:

The graph:

Piecewise:

The solution