Question 1157536
<pre>

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:

{{{f(x) = ln(x)}}},

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

{{{"f'(x)"=(1/x)/ln(x) = (1/x)(1/ln(x))=1/(x*ln(x))}}}

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

{{{ int( 1/(x*ln(x)),dx) = ln(ln(x)) + c}}}

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

{{{int(1/(x*"f(x)"),dx) = "f(f(x))" + c)}}} 

were true.  But that IS GIVEN true, so  

{{{"f(x)"=ln(x)}}}

must be true. 

PROVED!

Edwin</pre>