How Do You Solve Complex Integrals Using the Error Function?

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rpand4
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I have this question that I have been stuck on for quite sometime. If someone could assist me in solving it then that would be great. Can someone please shed some light?

I have attached the question in a document.

Thankyou
 

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To get started insert the integral definition of the error function into the integral you are doing. View this as a double integral over an area in u,x space. Then look at different ways to evaluate this double integral.