# Question about integral and natural log

1. Sep 13, 2011

### JamesGoh

1. The problem statement, all variables and given/known data

Find the integral to the following expression

$\int\frac{1}{x-1}dx$

2. Relevant equations

$\int udv = uv - \int vdu$

$\int\frac{1}{x}dx = ln(x)$

3. The attempt at a solution

Given the information above, would a correct answer to this problem be ln(x-1) ? If not, what am I doing wrong ?

thanks

2. Sep 13, 2011

### lanedance

how non need to use int by parts a simple substitution will do, ln(x-1) is correct

if you don't show what you doing (your steps it woudl eb hard to tell what was going wrong as well ;)

3. Sep 13, 2011

### JamesGoh

oh i just realised if you use substitution of variable u=x-1, it makes it easy to show that integral of 1/(x-1) is ln(x-1) :)

Last edited: Sep 13, 2011
4. Sep 13, 2011

### lanedance

good guess, is that all you need?

5. Sep 13, 2011

### stallionx

You can attack the problem as follows

let F(x)=$\int\frac{1}{x-1}dx$

From then on make substitution x=x+1

which yields

F(x+1)=$\int\frac{1}{x}dx$

Find out this integral which is quite obvious ( do not forget to add a constant to it )

since what you found is F(x+1) now re-substitute x=x-1

6. Sep 13, 2011

### JamesGoh

yeah pretty much. i worked it out myself using the substituiton and it came out fine

7. Sep 13, 2011

### Hootenanny

Staff Emeritus
:grumpy:

8. Sep 13, 2011

### lanedance

agree, would always use a different variable to represent the substitution eg. u = x-1, then du = dx