Question

Could someone please help me with the following integral?

Answer 1

\[\int\limits_{0}^{\infty}\cos(\omega t)e ^{-st}dt\]

Answer 2

you could replace cos(wt) with e^(i w t)
integrate, then take the real part

Answer 3

Or IBP twice

Answer 4

I did IBP twice and got stuck, the original integral doesn't cancel well.

Answer 5

as you know
e^( i w t ) = cos(wt) + i sin(wt)

it turns out we can put in e^(i w t) , do the integration
then look at the real part.

Answer 6

and, btw, the imaginary part of the answer will be equivalent to integrating sin(wt) e^(-st)

Answer 7

nvm i got it with ibp