Question

how to solve the integral of e^(-st)tcos(3t)dt

Answer 1

Are you trying to integrate: \[\int\limits e^{-st} *t *\cos(3t)* dt\]

Just making sure there aren't any typos.

Answer 2

yes

Answer 3

I'd use integration by parts here. First off, you have to decide which piece you want to differentiate and which piece to integrate.

Well, no matter what you choose it's gonna be a little messy. But you should pick:

t=u and e^(-st)cos(3t)dt=dv

That way your t goes away and you can solve the other integral.

Answer 4

i didnt realize u can do intergration by parts with 3 functions

Answer 5

Yeah, you just have to choose your function to be multiple functions multiplied together like I did there.

Answer 6

so once i solve using intergration by parts and get rid of the t i have to use it again

Answer 7

Kind of, although the integral you have to solve to do integration by parts requires integration by parts. So you might already have the answer previously from solving it if that makes sense. There's a lot of integration going on here haha.

Answer 8

lol

Answer 9

so i going to try out the method

Answer 10

I'll check whatever you put up here.

Answer 11

sounds good

Answer 12

but it might take a while lol

Answer 13

lol it seems it gets worst...

Answer 14

now i get ((te^(-st))/(s^2+9))(-scos(3t)+3sin(3t))+c-Intergration of (e^(-st)/s^2+9)(-scos(3t)+3sin(3t))

Answer 15

Yep, that's it. Then just finish off that integral. You already have the answer to the cosine part.