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Tough integration question

http://www2.imperial.ac.uk/~bin06/M2PM3-Complex-Analysis/m2pm3exam(10).pdf

3(i).

How is this done? I know that we turn the product of the two integrals into a double integral but then what? The double integral is not nice.
Reply 1
If your double integrak looks like sx1txes+tdsdt\int \int s^{x-1} t^{-x} e^{-s+t} \,ds \,dt then the substitution u = s / t should work. (Easier to consider it as s = ut).

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