How Can I Integrate (sin t)(e^-st) by Parts?

[Jerimy240]

f(t)={sin t, 0<t<pie
0, t>pie}

After integrating (sin t)(e^-st) by parts I get

-1/s(sin t)e^-st + 1/s Integral[(e^-st (cos t)dt]

Looks like I'll be integrating forever. I'm I missing something?

Also, is there software you can install to help you type math symbols so I can interact on this forum more efficiently?

 

[HallsofIvy]

Yes, you are integrating
$$\int_0^{\pi} e^{-st}sin(t)dt$$
and if you use integration by parts with you will, after a couple of integrations get something like
$$\int_0^{\pi} e^{-st}sin(t)dt= F(s)- C\int_0^\pi e^{-st}sin(t)dt$$

Now add that integral to both sides:
$$(1+ C)\int_0^{\pi} e^{-st}sin(t)dt= F(s)$$

 

[Jerimy240]

Thanks HOI, the final answer is (1+e^-spie)/(s^2 + 1) I don't know how to get there

 

[vela]

Do one more integration by parts and then look at HallsofIvy's suggestion again.