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

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

The solution

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

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

Integral(x^2 - 6*x - 5, (x, 1, 5))

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:
    
    $\int \left(- 6 x\right)\, dx = - 6 \int x\, dx$
    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]

-152/3

$$- \frac{152}{3}$$

-152/3

$$- \frac{152}{3}$$

-152/3

Numerical answer [src]

-50.6666666666667

-50.6666666666667

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

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

Limits of integration:

The graph:

Piecewise:

The solution