Help Solving Integration $\int_{-\infty}^{\infty} {(\text{Standard Normal} \times \text{Sigmoid}) }$
How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$