# Integrating a logarithmic function

1. May 2, 2004

### Math Is Hard

Staff Emeritus
I noticed than in the chapters I am studying now that while they give us a formula for taking the derivative of log base a of x, I can't find a correspoding formula for finding the integral of log base a of x.
We have a table of integrals in the back of the book, but I only see integrals pertaining to forms of ln x.
So.. am I missing something? Does it not exist? Is it something so ugly I don't even want to know about it??

Thanks!

2. May 2, 2004

$$\log_a{x} = \frac{\ln{x}}{\ln{a}}$$

3. May 2, 2004

### Math Is Hard

Staff Emeritus
ok, so I use change of base to convert. Then to integrate, do I use substitution, or is it simpler than that? thanks.

4. May 2, 2004

ln(a) is a constant. It comes right out front.

5. May 3, 2004

### Math Is Hard

Staff Emeritus
Oh crud! I walked away from the computer after my last post and then all of a sudden it hit me like a ton of bricks!!!
thanks, CM. You are going to be a big hit at CalTech.