Is the Integral of 3/x Equal to 3lnx?

[cabellos6]

Homework Statement

the integral of 3/x

Homework Equations

The Attempt at a Solution

am i right in saying this is 3lnx

 

[Kurdt]

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

 

[quantumdude]

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

 

[Kurdt]

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

Indeed

Welcome back Tom!

 

[rxtrejo]

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

 

[Hootenanny]

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

Well, what do you think it is?

 

[NJunJie]

rxtrejo - you asking a question?

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

 

[Mark44]

rxtrejo - you asking a question?

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

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

 

[Mark44]

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.