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Graphing y =:
-x^2+5*x-6
Identical expressions
-x^ two + five *x- six
minus x squared plus 5 multiply by x minus 6
minus x to the power of two plus five multiply by x minus six
-x2+5*x-6
-x²+5*x-6
-x to the power of 2+5*x-6
-x^2+5x-6
-x2+5x-6
-x^2+5*x-6dx
Similar expressions
-x^2-5*x-6
x^2+5*x-6
-x^2+5*x+6

Integral of -x^2+5*x-6 dx

The solution

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  0                    
  /                    
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 |  /   2          \   
 |  \- x  + 5*x - 6/ dx
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0

$$\int\limits_{0}^{0} \left(\left(- x^{2} + 5 x\right) - 6\right)\, dx$$

Integral(-x^2 + 5*x - 6, (x, 0, 0))

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:
    
    $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
    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: $- \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 5 x\, dx = 5 \int x\, dx$
    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:
  
  $\int \left(-6\right)\, dx = - 6 x$
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]

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

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

Simplify

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Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Integral of -x^2+5*x-6 dx

Limits of integration:

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Piecewise:

The solution