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.