How to express the function "1/(exp(x^2)-1)"

2

This

t\geq \frac{1}{e^x-1},\quad x>0

is equivalent to

1\geq e^{-x}+\frac{1}{1+t}

which can be written almost verbatim

1 >= exp(-x) + inv_pos(1+t)

However your variant with x^2 seems much harder. Maybe you can reformulate the whole model somehow to avoid the square.