I am a PhD student (not in maths). I have recently encountered a problem in my research which requires a solution to the following integral question:

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Let:

Find an expression or approximate expression of several terms for the following integral:

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It looks like a classical question, and must have been solved by mathematicians long time ago. However I am not a maths student, so I don't know.

If someone in this forum knows, please tell me. Exact solution or approximate solution with several terms are all OK.

Any solution must be in general form involving those 4 parameters.

Or please tell me about any journal article or maths textbook that discuss this question or similar question. Thank you!