when doing integration by parts, should we stick to the same "values" of u and v; or, can we swap strategy if another integral pops up that can be solved in the alternate order?
if that makes no sense, just ask
That makes some sense, but I'm not sure I entirely understand the question. There are one or two ambiguities.
when doing IBPs there tends to be a new integral that pops up at the ned to work on; can that integral be determined according to its own setup; or do we have to follow the setup we began with and derive u and integrate v?
if i'm understanding you properly....basically your asking if at first we start with uv - vdu, and when that's solved you want to do something such as basic u subsitution?
there are times when we have to do multiple IBPs; since the laggard on the end doesnt like to behave itself
the int: v du part
There's no requirement that you continue using the same substitution, but just make sure you keep track of what you are subbing for what.
If you can give an example it might help explain
:) it would help, but its just a random thought ....
i've worked with certain situations such as e^2x when integrating having to take the derivative in order to make it work
so i don't think your limited to what you have to do to grind it out so to speak...again..a.ssuming i understand what your saying
if you find the solution that is equal to what you intergrate you take that solution to be on the same side of what you are intergrating so that you'll add them to give u one value. if you don't get me youcan email your question to email@example.com
remainder, thats correct; and a good concept to keep in mind.
when a set up a table for my IBPs i tend to follow the u side down: u, u', u'', ... and the vside up; int v, int' v, int'' v, ... and on certain examples it messes me up.
x sin-1(x) might be a good example:|dw:1314378072284:dw|
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