I want to convert an integral from $(t_0, \infty)$ (or $(-\infty, t_0)$) range to $(-\infty, \infty)$ range by change of variable. What is the best transform function to do this - one that is simple, monotonic with $f(-\infty)=t_0$ and $f(\infty)=\infty$ (or $f(-\infty)=-\infty)$ and $f(\infty)=t_0$)?
I need this for an application of numerical quadrature with Gaussian weights.
Thanks.