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On the bottom of page 24 & top of page 25 of this pdf an integral is beautifully computed by breaking it up into an infinite series. Is there any reference where I could get practice in working integrals like these?

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There are many problems which are solved this way. I can provide you one I worked recently. The problem is to integrate from 0 to T, (1- x)^a / x, where "a" is irrational. I give you the first trick : make a change of variable : x = 1 - y; expand the denominator as an infinite series, integrate and ... come back to me. The result is a special function which is not in the pdf but we could speak later about it (if you like this problem, for sure !). Enjoy !

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