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

[pb23me]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[DivisionByZro]

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

 

[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?

 

[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.

 

[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 ?

 

[pb23me]

ok thanks guyz I precciate ya!

 

[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'.