is this conjecture true or false? I want to know if this conjecture istrue or false
$$\Large e^{\frac{ \ln x}{x}} \notin \mathbb{Z} $$
for every $x \in \mathbb{R} \setminus \{1,-1,0\} $

Just like Oliver Bel said, $e^{lnx/x} = x^{1/x}$.
Now, suppose there exist an integer N such that $N^x=x, N>1$. Try to graph the equations $y = N^x$ and $y = x$. It should be clear that no such integer exists.
