Mister Exam

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Integral of d{x}:
Integral of 3
Integral of x^n
Integral of -3
Integral of sec^3(x)
Factor squared:
x^2+x-6
Equation:
x^2+x-6
Graphing y =:
x^2+x-6
Identical expressions
x^ two +x- six
x squared plus x minus 6
x to the power of two plus 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
x^2+x+6

Solving integrals/ x^2+x-6

Integral of x^2+x-6 dx

The solution

You have entered [src]

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

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

Integral(x^2 + x - 1*6, (x, -3, 2))

Detail solution

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 $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(\left(-1\right) 6\right)\, dx = - 6 x$
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 
/

$${{x^3}\over{3}}+{{x^2}\over{2}}-6\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-125/6

$$-{{125}\over{6}}$$

-125/6

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

Упростить

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