What is the integral 1/x log(x) or lnx?

1. Oct 26, 2011

pb23me

1. The problem statement, all variables and given/known data
I know it is supposed to be lnx however I find something peculiar. When I integrate it in wolfram alpha they give the integral as log(x). What the heck is going on here!?!

2. Relevant equations

3. The attempt at a solution

2. Oct 26, 2011

DivisionByZro

If you check closer on Wolfram, by log(x) they mean the natural logarithm.

3. Oct 26, 2011

pb23me

ok thanks, When looking at more complex solutions sometimes there are many logx's how am I supposed to know which one is logx and which one is not really logx?

4. Oct 26, 2011

DivisionByZro

They will usually define what they use. As a rule of thumb, I find that they always tend to use the natural log, but it could happen that they don't. Just pay attention to the bottom of the equation box thingy.

5. Oct 26, 2011

Highway

the derivative of ln(x) is "one over the thing inside, times the derivative of the thing inside" -- my calc professor

so, y = ln (x); y' = 1/x * 1 = 1/x

i'm not sure if this helps or not... you are asking for y given y' = 1/x ?

6. Oct 26, 2011

pb23me

ok thanks guyz I precciate ya!

7. Oct 26, 2011

dextercioby

It's simple. The 'Mathematica' software developed by Wolfram himself or his company has the natural logarithm (aka neperian logarithm) denoted as LOG, instead of the widely used LN which is derived from <natural logarithm> spelled in Latin. Most people use LOG for the logarithm in other base than Euler's number 'e'.