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I'm self-studying MIT 18.03. I have come across a topic, the complexification of integrals, and would like to do practice questions involving this topic. I cannot find any questions pertaining to the topic in any calculus textbook, or differential equation textbook I have. Can someone point me to a textbook or other resource which contains questions on this topic?

user112167
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    The book "Fundamentals of Complex Analysis" by E B Saff and Arthur David Snyder is pretty good. – Doug Aug 23 '22 at 16:24
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    I don't think complex contour integrals are intended here. Can you please be explicit about what "complexification of integrals" means to you? My guess is that you want to play with things like $\int e^{ix},dx$ and $\int e^{ix}f(x),dx$. – Ted Shifrin Aug 23 '22 at 16:30
  • @TedShifrin I'm not exactly sure which type Professor Mattuck meant in the lecture, he called it complexifying the integral. He used the formula $e^(ix)=cos(x)+isinx$ to solve the integral $int(e^(-x)cos(x)dx)$ – user112167 Aug 23 '22 at 16:35
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    Wow! I don't think I've seen this before... pretty cute technique. https://en.wikibooks.org/wiki/Calculus/Integration_techniques/Integration_by_Complexifying – Doug Aug 23 '22 at 16:39
  • "Complexification" sounds like it's just a matter of replacing $\cos(x)=\frac{e^{ix}+e^{-ix}}2$ and $\sin(x)=\frac{e^{ix}-e^{-ix}}2$. Then$$\int e^{-x}\cos(x),dx=\frac12\int (e^{(-1+i)x} + e^{(-1-i)x}) , dx$$ – user170231 Aug 23 '22 at 16:59

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