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Integral of d{x}:
Integral of x^2
Integral of sin^3xdx
Integral of cos(y)^(-2)
Integral of x^2sinx^3dx
Graphing y =:
x^2-5x+6
Canonical form:
x^2-5x+6
Identical expressions
x^ two -5x+ six
x squared minus 5x plus 6
x to the power of two minus 5x plus six
x2-5x+6
x²-5x+6
x to the power of 2-5x+6
x^2-5x+6dx
Similar expressions
x^2-5x-6
(x+5)/((x^2-5*x+6)(1+1))
x^2+5x+6

Solving integrals/ x^2-5x+6

Integral of x^2-5x+6 dx

The solution

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  3                  
  /                  
 |                   
 |  / 2          \   
 |  \x  - 5*x + 6/ dx
 |                   
/                    
2

$$\int\limits_{2}^{3} \left(\left(x^{2} - 5 x\right) + 6\right)\, dx$$

Integral(x^2 - 5*x + 6, (x, 2, 3))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  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: $\frac{x^{3}}{3} - \frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 6\, dx = 6 x$
The result is: $\frac{x^{3}}{3} - \frac{5 x^{2}}{2} + 6 x$
Now simplify:

$\frac{x \left(2 x^{2} - 15 x + 36\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 15 x + 36\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 15 x + 36\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                  2    3
 | / 2          \                5*x    x 
 | \x  - 5*x + 6/ dx = C + 6*x - ---- + --
 |                                2     3 
/

$$\int \left(\left(x^{2} - 5 x\right) + 6\right)\, dx = C + \frac{x^{3}}{3} - \frac{5 x^{2}}{2} + 6 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/6

$$- \frac{1}{6}$$

-1/6

$$- \frac{1}{6}$$

-1/6

Numerical answer [src]

-0.166666666666667

-0.166666666666667

The graph

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

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Identical expressions

Similar expressions

Integral of x^2-5x+6 dx

Limits of integration:

The graph:

Piecewise:

The solution