Question

Question regarding IBP Methods.

If I have the integral (t^7)(sin(2t^4)dt

Does the table method give you same answer as when using substitution?

Answer 1

maybe start by substituting 2t^4 = u

Answer 2

I got the answer using substitution (1/16)(sin(2t^4) - (1/8)(t^4)cos(2t^4) + C

I got another answer by the table method without C

( (7/64) - (105/2048(t^8)) + (315/(32768t^16)) ) (sin(2t^4)) +
( (-t^4)/8 + (21/(256t^4)) - (105/(4096t^12)) + (315/(131072t^20)) (cos(2t^4))

Answer 3

The question is are they both working or is there a rule with the table method that makes it work only in certain situations like partial fraction differentiation and long division have?

Answer 4

I know the first one works...

it is hard for me to know how you got that table answer without a table :p

Answer 5

but yes answers for indefinite integrals can take on different looking forms and still be equivalent
and since this is a indefinite integral you should have +constant even if that answer did come from a table

Answer 6

What @freckles said. Keep in mind that there are a lot of trigonometric identities, and that you can reach an apparently different answer that is really the same. For instance, we know that sec^2 x=1+tan^2 x... well, someone might get tan^2 x+C for a problem and you might get sec^2 x+C for a problem... just means the two constants are "absorbing" the 1 in this case.