Integral of 1/(x-2) dx

The solution

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

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

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

Detail solution

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:

$\log{\left(x - 2 \right)}$
Now simplify:

$\log{\left(x - 2 \right)}$
Add the constant of integration:

$\log{\left(x - 2 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(x - 2 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                            
 |     1                      
 | 1*----- dx = C + log(x - 2)
 |   x - 2                    
 |                            
/

$$\log \left(x-2\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(2)

$$-\log 2$$

-log(2)

$$- \log{\left(2 \right)}$$

Упростить

Numerical answer [src]

-0.693147180559945

-0.693147180559945

The graph

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

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Integral of 1/(x-2) dx

Limits of integration:

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Piecewise:

The solution