Does $\int\frac{1}{2}\tanh\left(\frac{1}{x^{2}}\right)\,dx$ have a closed form? Context: I am looking for an activation function that is linear in the area surrounding $x=0$, while also staying within the range of -1 to 1. While I was messing around in Desmos, I stumbled across the function $f(x)=\frac{1}{2}\tanh\left(\frac{1}{x^{2}}\right)$.
$\int\frac{1}{2}\tanh\left(\frac{1}{x^{2}}\right)\,dx$ produces the exact shape I am looking for, but I cannot figure out how to find the closed form for it. 
Am I missing something obvious, or does this function not have a closed form antiderivative?

Simplest one I can think of is
$\dfrac{x}{1+|x|}
$.
There are also
$\tanh(x)
$
and
$\arctan(x)
$
scaled as
$(2/\pi)\arctan(\pi x/2)
$.
