Right so, here is what i would like to find out:

L( cosbx) , where L(f(x)) means the Laplace Transform of that function; i is the imaginary unit.

That would equal to = = = (taken from 0 to infinity) (taken from 0 to infinity) ) = (taken from 0 to infinity) (taken from 0 to infinity)) = =

But the problem is that it says the Laplace transform for that function is supposed to be

With that having been said and since i put up the way i solved it, i have the following question:

1) Where did i go wrong in the way i solved it?

2) What does 'p' represent in the Laplace transform ? ( i realise i should know that, but i do not and would be thankful if someone told me what it represents)

3) Why, when you calculate the integral here (taken from 0 to infinity) (taken from 0 to infinity) 0, do you put the mnus sign in front of the paranthesis, thus changing the signs of the variables and not just leave it (taken from 0 to infinity) (taken from 0 to infinity) 0? Can the p not be negative? If you were to not move the minus sign out of the paranthesis, it would lead to and infinity case?

4) I did not know how to make the sign (taken from 0 to infinity) in LaTex. Could someone post it up in a post, please?

I would greatly appreciate help on this matter, thank you in advance!