I'm trying to solve this expression when $b \ne 0$:
$$ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $$
Using the answers provided to this question we can solve $$\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-x}}\,\mathrm dx=\frac12$$
However, when we change the power of exponential term in the denominator to $-(ax+b)$ from $x$, the expression can not be solved using the same methods used in the post. I tried solving by substituting $z=ax+b$ and it also did not work.