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

Solving integrals/ x^2-x-6

Integral of x^2-x-6 dx

The solution

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  3                
  /                
 |                 
 |  / 2        \   
 |  \x  - x - 6/ dx
 |                 
/                  
-2

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

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

$\frac{x \left(2 x^{2} - 3 x - 36\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 3 x - 36\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 3 x - 36\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-125/6

$$- \frac{125}{6}$$

-125/6

$$- \frac{125}{6}$$

-125/6

Numerical answer [src]

-20.8333333333333

-20.8333333333333

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-x-6 dx

Limits of integration:

The graph:

Piecewise:

The solution