Question 1176045
<pre>
{{{ln (x*sqrt(x^2+1))/e^x }}} ( = {{{ ln(x*(x^2+1)^(1/2)) / e^x }}} )
= {{{ (ln(x) + (1/2)ln(x^2+1)) / e^x }}} 

If you must expand further:
= {{{ ln(x)/e^x + (1/(2e^x))ln(x^2+1) }}}

or 
= {{{ e^(-x)ln(x)+ e^(-x)(1/2)ln(x^2+1) }}}