4 ms·
Probably the second example here [1] for those curious (I think the integral of sin(x)*e^x dx is the only place I've seen this used, would love to know if there
by mattb314 11y ago
Probably the second example here [1] for those curious (I think the integral of sin(x)*e^x dx is the only place I've seen this used, would love to know if there are other examples).
[1] https://en.m.wikipedia.org/wiki/Integration_by_parts#Tabular_integration_by_parts https://en.m.wikipedia.org/wiki/Integration_by_parts#Tabular...
- octonion 11y agoThis becomes much more transparent if you realize you're integrating Im(e^x * e^{ix}). And it's no longer a trick but a technique.
- AstralStorm 11y agoIt becomes a technique once you realise it is a specific case of change of bases. Even just getting to basic theorem of algebra does not provide this insight.
- vcarl 11y agoIt would be great if that were how it was taught, but when I took the class it was taught as a trick. No theory behind it, just the prof on the board saying, "But look! :swap: And now you can integrate it."