Integral of (-1)/(x-1) dx

The solution

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  4         
  /         
 |          
 |   -1     
 |  ----- dx
 |  x - 1   
 |          
/           
3

$$\int\limits_{3}^{4} \left(- \frac{1}{x - 1}\right)\, dx$$

Integral(-1/(x - 1), (x, 3, 4))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \left(- \frac{1}{x - 1}\right)\, dx = - \int \frac{1}{x - 1}\, dx$
1. Let $u = x - 1$ .
  
  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:
  
  $\log{\left(x - 1 \right)}$
So, the result is: $- \log{\left(x - 1 \right)}$
Now simplify:

$- \log{\left(x - 1 \right)}$
Add the constant of integration:

$- \log{\left(x - 1 \right)}+ \mathrm{constant}$

The answer is:

$- \log{\left(x - 1 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(3) + log(2)

$$- \log{\left(3 \right)} + \log{\left(2 \right)}$$

-log(3) + log(2)

$$- \log{\left(3 \right)} + \log{\left(2 \right)}$$

-log(3) + log(2)

Numerical answer [src]

-0.405465108108164

-0.405465108108164

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

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Integral of (-1)/(x-1) dx

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The solution