Integral of error function, normal distribution and x

[User20202020]

Hello all.
I am trying to integrate the following function

[MATH]\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[/MATH]

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!

 

[HallsofIvy]

I would recommend starting with the substitution \(\displaystyle y= A\frac{x- \mu}{\sigma}\).
The "A" will pop up in the exponential but it is more easily handled there.

 

[User20202020]

Hello. I have tried solving the integral using you approach. However, I am not able to solve it I am afraid. Would you be so kind as to please provide me with the solution? I have been working on a particular project for 6 months now and this integral appears to be one of the only steps left to find a solution. So if you would be so kind as to give me the answer, I would be extremely grateful. Thank you

 

[Deleted member 4993]

Hello. I have tried solving the integral using you approach. However, I am not able to solve it I am afraid. Would you be so kind as to please provide me with the solution? I have been working on a particular project for 6 months now and this integral appears to be one of the only steps left to find a solution. So if you would be so kind as to give me the answer, I would be extremely grateful. Thank you

Please show your work (mathematically) - following the suggestion in response #2 (even if you are sure that it is not going anywhere). We can correct your mistake (if there is any) and guide you correct path.

We need to see your work - before we can help you.

 

[User20202020]

Please show your work (mathematically) - following the suggestion in response #2 (even if you are sure that it is not going anywhere). We can correct your mistake (if there is any) and guide you correct path.

We need to see your work - before we can help you.

Here is my working :






Oh wait. I don't actually care. Please could you KINDLY provide me with the answer, as you clearly know how to get it. I have been working on a problem for 6 MONTHS and this is the last step to a complete solution. I have no experience in higher level calculus, and right now I have no interest in learning it either. I just want the answer. Please would you kindly.

 

[Deleted member 4993]

Here is my working :
Oh wait. I don't actually care. Please could you KINDLY provide me with the answer, as you clearly know how to get it. I have been working on a problem for 6 MONTHS and this is the last step to a complete solution. I have no experience in higher level calculus, and right now I have no interest in learning it either. I just want the answer. Please would you kindly.

Oh wait. I don't actually care.

I don't either

Hello. I have tried solving the integral using you approach.

Did you REALLY try - or just making conversation?!!