# Homework Help: Laplace Transform question

1. Jul 20, 2011

### trojansc82

1. The problem statement, all variables and given/known data

Laplace Transform of e-t sin t

2. Relevant equations

3. The attempt at a solution

I have the solution, but I am unable to figure out how the denominator becomes 1/[(s + 1)2 + 1]

2. Jul 20, 2011

### rock.freak667

The presence of the eat would case the shift from 's' to 's-a'. This is why it is called the shift theorem, it's mainly used in the inverse laplace transform.

So you know that L{sint} = 1/(s2+1)

and following shift theorem L(eatsint) = 1/[(s-a)2+1].

You can derive it too using the integral formula.

3. Jul 20, 2011

### trojansc82

I am unable to derive it from the integral formula. I need to see the steps. I'm fairly certain I've been able to integrate it correctly, but I keep getting a repetitive e^-t sin t or e^-t cos t when I integrate.

4. Jul 20, 2011

### Bohrok

So you're probably ending up with something like ∫e-t sin t dt on both sides of the equation; just move one to the other side and combine them as like terms. There's a good example of a similar problem on Wikipedia with ∫ex cos x dx:
http://en.wikipedia.org/wiki/Integration_by_parts#Integrals_with_powers_of_x_or_ex