# Math Help - Laplace transform.

1. ## Laplace transform.

Hi there, im struggling with this past exam question at the moment, is there anyone that can show me a complete working of it? Tried it a few times and belive i keep making minor errors.
Find the laplace transform of the following:

g(t)= (sin(5t))/e^6t

Even if someone can get the initial integration of the above I will hopefully be able to do the rest!
Thanks for any help,
Andy

2. Originally Posted by andymarra
Hi there, im struggling with this past exam question at the moment, is there anyone that can show me a complete working of it? Tried it a few times and belive i keep making minor errors.
Find the laplace transform of the following:

g(t)= (sin(5t))/e^6t

Even if someone can get the initial integration of the above I will hopefully be able to do the rest!
Thanks for any help,
Andy
I'ld start by writing g(t) as $g(t) = e^{-6t} \sin (5t)$ so that $LT[f(t)] = F(s) = \int_0^{+\infty} e^{-(s + 6t)} \sin (5t) \, dt$. Now use integration by parts. The answer can be checked using an appropriate standard operational theorem that you will undoubtedly find in your tables of laplace transforms.

If you need more help, please show all your work and say where you get stuck.