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Integrate initial arrangement

let me explain why it's it's it's it ruins a joke when you have to explain it right but anyway hopefully it is sufficient value to the rest of you that you got some um some community value out of it sure okay uh we're continuing on talking about integration bypass today as the heading suggests and i hope you've made the heading by now with my black mark ago now for me one of the things that was most perplexing when i first learned about integration by parts was why it's called the integration by parts because we know where integration by parts comes from rehearse it with me if you have some kind of function which is composed of the product of two other functions right when we're differentiating when you get presented with a product we know this is called it's called not a rhetorical question guys of the product rule thank you okay you differentiate a product imaginative right so we use the product rule now the product rule is most succinctly stated as v u dash plus u v dash but for the purposes of getting to this piece of knowledge in integration maybe you remember a more helpful way to say it might be v and then instead of writing u dash i'll go to leiden it says long form notation d u on dx that's a way of saying u dash plus u and then how would i write v dash d v on dx right so at this point here you are mere millimeters away from the statement the classic statement of integration by parts i'm going to write this like sort of dicey line in here i've referred to how dangerous it is to do what i'm about to do before because these d on dx's the u's and the x and that kind of thing they're not fractions you cannot just categorically treat them as fractions but under many of the circumstances we do use them you kind of can treat them like fractions so i'm going to do something here that looks like a pretty classic thing to do with a fraction i'm sort of going to imagine considering everything except you notice how everything here is with respect to x right i'm differentiating with respect to x you can see the differential operator there if i consider everything without this differential operator do you see where integration bypass leaks from now right the part that i want comes from integrating everything here with respect to x and then we do a bit of minor rearrangements so what am i going to get over here we take this uh actually it's not the v du it's classically it's the u dv what do i write over here just that udv right recognize this okay on the right hand side i've actually switched this over so i'm going to get this when i integrate that i just get u v...