Question

What would be the pros and cons of using a quotient rule integration by parts formula?

Answer 1

\[\int\frac{t'}{b}=\frac{t}{b}+\int\frac{bt'}{b^2}\]
or some such

Answer 2

shouldn't it be
\[\int\limits_{}^{}\frac{t'}{b}=\frac{t}{b}+\int\limits_{}^{}\frac{t}{b^2} ?\]

Answer 3

maybe ... it was a quick write up :)

Answer 4

\[\frac{t}{b}=\int\frac{t'}{b}-\int\frac{b't}{b^2}\]

Answer 5

oh wait maybe i should have said b'

Answer 6

ok i agree with your last equation

Answer 7

:) good, since its just the quotient rule lol

ive read that it is really just the product rule in a different form ..

Answer 8

its workable, just havent seen it done alot if ever

Answer 9

yes any quotient can be written as a product
really no need for the quotient rule

Answer 10

\[tb^{-1}=\int t'b^{-1}+\int tb'^{-1}\]
\[tb^{-1}-\int tb'^{-1}=\int t'b^{-1}\]

Answer 11

\[tb^{-1}=\int\limits_{}^{}t'b^{-1}-\int\limits_{}^{}b'b^{-2}t\]
\[\int\limits_{}^{}t'b^{-1}=tb^{-1}+\int\limits_{}^{}b'b^{-2}t\]

Answer 12

yeah, that looks contorted into shape :)

Answer 13

i like product rule more

Answer 14

i don't want to make one for quotient rule lol

Answer 15

i like only \[(fg)'=f'g+fg'\]
\[fg=\int\limits_{}^{}f'g+\int\limits_{}^{}fg'\]
\[\int\limits_{}^{}fg'=fg-\int\limits_{}^{}f' g\]