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Identical expressions
(x- two)/(x- two)
(x minus 2) divide by (x minus 2)
(x minus two) divide by (x minus two)
x-2/x-2
(x-2) divide by (x-2)
(x-2)/(x-2)dx
Similar expressions
(x-2)/(x+2)
(x+2)/(x-2)
e^(-0,25*0,03856*(x-2))/(x-2)

Integral of (x-2)/(x-2) dx

The solution

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  1         
  /         
 |          
 |  x - 2   
 |  ----- dx
 |  x - 2   
 |          
/           
0

$$\int\limits_{0}^{1} \frac{x - 2}{x - 2}\, dx$$

Integral((x - 2)/(x - 2), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{x - 2}{x - 2} = \frac{x}{x - 2} - \frac{2}{x - 2}$
Integrate term-by-term:
1. Rewrite the integrand:
  
  $\frac{x}{x - 2} = 1 + \frac{2}{x - 2}$
2. Integrate term-by-term:
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $x$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{2}{x - 2}\, dx = 2 \int \frac{1}{x - 2}\, dx$
    1. Let $u = x - 2$ .
      
      Then let $du = dx$ and substitute $du$ :
      
      $\int \frac{1}{u}\, du$
      1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
      Now substitute $u$ back in:
      
      $\log{\left(x - 2 \right)}$
    So, the result is: $2 \log{\left(x - 2 \right)}$
  The result is: $x + 2 \log{\left(x - 2 \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{2}{x - 2}\right)\, dx = - 2 \int \frac{1}{x - 2}\, dx$
  1. Let $u = x - 2$ .
    
    Then let $du = dx$ and substitute $du$ :
    
    $\int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    Now substitute $u$ back in:
    
    $\log{\left(x - 2 \right)}$
  So, the result is: $- 2 \log{\left(x - 2 \right)}$
The result is: $x - 2 \log{\left(x - 2 \right)} + 2 \log{\left(x - 2 \right)}$
Now simplify:

$x$
Add the constant of integration:

$x+ \mathrm{constant}$

The answer is:

$x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                                                
 | x - 2                                          
 | ----- dx = C + x - 2*log(x - 2) + 2*log(-2 + x)
 | x - 2                                          
 |                                                
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1$$

Numerical answer [src]

1.0

1.0

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-2) dx

Limits of integration:

The graph:

Piecewise:

The solution