Hello Mathematica Community,

I am working on a mathematical problem where I need to transform an integral equation into a simpler form using Euler's Formula and the Error Function. My current Mathematica code successfully simplifies the equation, but I'm looking for ways to extract more detailed intermediate steps within Mathematica.

The original equation is:

And it is transformed into:

I have used Euler's formula for the sine function and Mathematica provides the simplified result directly as:

However, I'm interested in understanding the intermediate steps that Mathematica goes through to arrive at this result. Specifically, I am looking for:

1. Mathematica techniques or functions that can help me break down the transformation process into more granular steps.
2. Insights into how Mathematica handles integral transformations, especially involving complex functions and the error function.
3. Any special Mathematica tricks or commands that could make these intermediate steps more explicit.

I would greatly appreciate any advice or guidance on how to use Mathematica more effectively for this purpose. Understanding the intermediate steps is crucial for my learning process.

Thank you for your help!