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

Solving integrals/ -x^2+6x-5

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

The solution

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  2                    
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 |  /   2          \   
 |  \- x  + 6*x - 5/ dx
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1

$$\int\limits_{1}^{2} \left(\left(- x^{2} + 6 x\right) - 5\right)\, dx$$

Integral(-x^2 + 6*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:
    
    $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
    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:
    
    $\int 6 x\, dx = 6 \int x\, dx$
    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: $3 x^{2}$
  The result is: $- \frac{x^{3}}{3} + 3 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-5\right)\, dx = - 5 x$
The result is: $- \frac{x^{3}}{3} + 3 x^{2} - 5 x$
Now simplify:

$\frac{x \left(- x^{2} + 9 x - 15\right)}{3}$
Add the constant of integration:

$\frac{x \left(- x^{2} + 9 x - 15\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- x^{2} + 9 x - 15\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/3

$$\frac{5}{3}$$

5/3

$$\frac{5}{3}$$

5/3

Numerical answer [src]

1.66666666666667

1.66666666666667

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution