# Laplace transforms

1. Apr 26, 2010

### Gogeta007

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

L{tcos(t)}

2. Relevant equations

Using the laplace transform find the equation.

3. The attempt at a solution

I already have a really long answer. . .I was just wondering if someone can explain this:

Another method (appart from using integration by parts multiple times) was mentioned by my professor, he said to take the partial with respect to s of the integral, which will then just leave the partial laplace transform of cos(t) which can be found trough tables

I remember he explained it but now that I think about it it doesnt make sense:

L {t cos(t)} = (int)infinity0 e-stt cos(t)dt
then you can take the partial with respect to s (d/ds) of that integral, and yo uwould end up with

d/ds [L{cost}] = d/ds [s/(s^2+1)]

cans omeone explain?
I remember he mentioned the potential function

2. Apr 27, 2010

### vela

Staff Emeritus
You use the fact that

$$te^{-st} = -\frac{\partial}{\partial s}e^{-st}$$

and then switch the order of integration and differentiation.