Mister Exam

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Integral of d{x}:
Integral of x/(x+2)
Integral of dx/(1+x^2)
Integral of x^2√(1-x^2)
Integral of log(x)^3/x
Graphing y =:
x^2-6x-7
Canonical form:
x^2-6x-7
Identical expressions
x^ two -6x- seven
x squared minus 6x minus 7
x to the power of two minus 6x minus seven
x2-6x-7
x²-6x-7
x to the power of 2-6x-7
x^2-6x-7dx
Similar expressions
x^2-6x+7
x^2+6x-7

Solving integrals/ x^2-6x-7

Integral of x^2-6x-7 dx

The solution

You have entered [src]

  7                  
  /                  
 |                   
 |  / 2          \   
 |  \x  - 6*x - 7/ dx
 |                   
/                    
-1

$$\int\limits_{-1}^{7} \left(\left(x^{2} - 6 x\right) - 7\right)\, dx$$

Integral(x^2 - 6*x - 7, (x, -1, 7))

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:
  
  $\int \left(-7\right)\, dx = - 7 x$
The result is: $\frac{x^{3}}{3} - 3 x^{2} - 7 x$
Now simplify:

$\frac{x \left(x^{2} - 9 x - 21\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 9 x - 21\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 9 x - 21\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                       3
 | / 2          \                   2   x 
 | \x  - 6*x - 7/ dx = C - 7*x - 3*x  + --
 |                                      3 
/

$$\int \left(\left(x^{2} - 6 x\right) - 7\right)\, dx = C + \frac{x^{3}}{3} - 3 x^{2} - 7 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-256/3

$$- \frac{256}{3}$$

-256/3

$$- \frac{256}{3}$$

-256/3

Numerical answer [src]

-85.3333333333333

-85.3333333333333

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-7 dx

Limits of integration:

The graph:

Piecewise:

The solution