# Integral of 3/x

1. Jan 14, 2008

### cabellos6

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

the integral of 3/x

2. Relevant equations

3. The attempt at a solution

am i right in saying this is 3lnx

2. Jan 14, 2008

### Kurdt

Staff Emeritus
Yes you are. Don't forget the arbitrary constant.

3. Jan 14, 2008

### Tom Mattson

Staff Emeritus
And don't forget the absolute value bars. It's 3ln|x|+C.

4. Jan 14, 2008

### Kurdt

Staff Emeritus
Indeed

Welcome back Tom!

Last edited: Jan 14, 2008
5. Sep 7, 2009

### rxtrejo

Same question adding Limits of integration b=infinity a=0

6. Sep 7, 2009

### Hootenanny

Staff Emeritus
Well, what do you think it is?

7. Sep 7, 2009

### NJunJie

rxtrejo - you asking a question?

That would mean substituting the bounded values and find some 'area' within the limits you have given.

8. Sep 7, 2009

### Staff: Mentor

Not so fast. This is an improper definite integral that requires limits at both endpoints to evaluate.

9. Sep 7, 2009

### Staff: Mentor

IOW,
$$3\int_0^{\infty} \frac{dx}{x} = 3\lim_{a \rightarrow 0_+}\int_a^{1} \frac{dx}{x}~+~ 3\lim_{b \rightarrow \infty}\int_1^{b} \frac{dx}{x}$$

I chose to split the first integral at 1. Any reasonable value could be used to divide the original interval into two subintervals.