This is $\int\frac{dx}{\operatorname{\\erf(x)}}$ a simple form integral which i can't to evaluate using variable change and integration by part to get it's form, but some computations in wolfram alpha coming up to me to know one side of it's behavior over the range $(1,n)$ with $n$ is a positive integer such that i have deduced this relation from some computation which i run :

$$\int_1^n \frac{dx}{\operatorname{\\erf(x)}}= n -\alpha$$ with $\alpha \sim 0.944974758233 \cdots $ and $n >1$ , Now my question here is :

Is really what have got true ? and is this function can be expressed as elementary function ?