SOLUTION: Prove that : If int(1/(xf(x)) dx = f(f(x)) + c then f(x) = ln(x)

We work backwards using "if and ONLY if" between steps:

First we only observe (not assume!!) about the answer we are supposed to get,
which is this:

,

that we could have gotten that if and ONLY if this were true:



And we could have gotten that if and ONLY if this were true:



But we know that would have been true if and ONLY if

 

were true.  But that IS GIVEN true, so  



must be true. 

PROVED!

Edwin