# Laplace Transformations help me please?

1. Dec 3, 2009

### yusukered07

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

Find the laplace transformations of the following:

a. $$\sin\, {\sqrt\,{x}}$$

b. $$\frac{\cos\,{\sqrt{x}}}{{\sqrt{x}}}$$

c. $$\ erf\,{(t)}^\frac{1}{2}}$$

d. $$\int_{t}^\infty\;\frac{\cos\,x}{x}\$$

e. $$\int_{t}^\infty\;\frac{{e}^{-x}}{x}\$$

2. Relevant equations.

3. The attempt at a solution

I used some properties of Laplace transformations, integration methods but still, didn't work.

Last edited: Dec 3, 2009
2. Dec 3, 2009

### ApexOfDE

Re: Laplace Transformations.... help me please?

are you sure about interval in prob d. and e.? I think it should be [t, inf].

3. Dec 3, 2009

### yusukered07

Re: Laplace Transformations.... help me please?

yeah... sorry typographical error.. It should be from t to infinity. Thanks!

4. Dec 3, 2009

### ApexOfDE

Re: Laplace Transformations.... help me please?

+++ For (d):
You have f(t) ==> f'(t) = -cost / t ==> tf'(t) = -cost
Now, find Laplace transform in both side and use final theorem, differentiation properties to find F.

+++ (e) is similar to (d)

p/s: trying to solve (a) :(

5. Dec 3, 2009

### yusukered07

Re: Laplace Transformations.... help me please?

d is called cosine integral right?

and e is exponential integral?

6. Dec 3, 2009

### ApexOfDE

Last edited by a moderator: Apr 24, 2017