IBP tabular method

[markraz]

Question for y'all
I noticed with tabular method if you have something like e^x sin(x) or e^2x sin(2x) or e^2x sin(2x) ....
you can use either e or the trig function as the U or the V.
does anyone know which is preferred? Should you always use the
trig ?? or e ?? as the U variable? Is one order more efficient?

thanks

 

[Ishuda]

Question for y'all
I noticed with tabular method if you have something like e^x sin(x) or e^2x sin(2x) or e^2x sin(2x) ....
you can use either e or the trig function as the U or the V.
does anyone know which is preferred? Should you always use the
trig ?? or e ?? as the U variable? Is one order more efficient?

thanks

Personally I don't really think there is any advantage one way or the other. However, I would use a substitution t=2x, ... for the equations like e^2x sin(2x) to keep those 2ⁿ and 2^-n factors from hanging around doing nothing but being (partially) canceled.

 

[markraz]

thank you