# Help with integrating a function

### Help with integrating a function

Hello all.
I am trying to integrate the following function
$$\frac{1}{\sigma\sqrt{2\pi}}\int^S _{-\infty} x \cdot\exp\left(\frac{-{\left(x-\mu \right)}^{2}}{2\sigma }\right)\cdot \operatorname{erf}\left(\frac{A(x-\mu )}{\sigma \sqrt{2}}\right)\mathrm dx$$
Without the parameter A, which is a variable for the "skewness" of a probability distribution, I have found results. However I am unable once it is included. Please help me integrate it if you are able to. Approximations (if you are unable to solve it) are also highly appreciated. This integral is very important for something I am working on so I will be extremely grateful for any help!
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