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Graphing y =:
1/(x-6)
Identical expressions
one /(x- six)
1 divide by (x minus 6)
one divide by (x minus six)
1/x-6
1 divide by (x-6)
1/(x-6)dx
Similar expressions
((sqrt(x))*1)/(x-6)
1/(x+6)
1/((x-6)(x-1))

Solving integrals/ 1/(x-6)

Integral of 1/(x-6) dx

The solution

You have entered [src]

  1         
  /         
 |          
 |    1     
 |  ----- dx
 |  x - 6   
 |          
/           
0

$$\int\limits_{0}^{1} \frac{1}{x - 6}\, dx$$

Integral(1/(x - 6), (x, 0, 1))

Detail solution

Let $u = x - 6$ .

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:

$\log{\left(x - 6 \right)}$
Now simplify:

$\log{\left(x - 6 \right)}$
Add the constant of integration:

$\log{\left(x - 6 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(x - 6 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                          
 |   1                      
 | ----- dx = C + log(x - 6)
 | x - 6                    
 |                          
/

$$\int \frac{1}{x - 6}\, dx = C + \log{\left(x - 6 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(6) + log(5)

$$- \log{\left(6 \right)} + \log{\left(5 \right)}$$

-log(6) + log(5)

$$- \log{\left(6 \right)} + \log{\left(5 \right)}$$

-log(6) + log(5)

Numerical answer [src]

-0.182321556793955

-0.182321556793955

The graph

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

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Identical expressions

Similar expressions

Integral of 1/(x-6) dx

Limits of integration:

The graph:

Piecewise:

The solution