Laplace Transformations help me please?

[yusukered07]

Laplace Transformations... help me please?

1. Homework Statement .

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. Homework Equations .


3. The Attempt at a Solution


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

 

[ApexOfDE]

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

 

[yusukered07]

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

 

[ApexOfDE]

+++ 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) :(

 

[yusukered07]

d is called cosine integral right?

and e is exponential integral?

 

[ApexOfDE]

yeah. For (a), use Taylor series for sinx (http://www.wolframalpha.com/input/?i=taylor+sin(sqrt(x))") and use nth power result.