# Thread: Substitution when doing Laplace transforms

1. ## Substitution when doing Laplace transforms

Hi,

I'm doing a coursework on Laplace transforms and a lecturer mentioned that we would have to use substitution for it. I'm not asking for help with answering the question but I don't understand how you're supposed to do substitution.

Any help would be much appreciated!

2. ## Re: Substitution when doing Laplace transforms

Originally Posted by uhm
Hi,

I'm doing a coursework on Laplace transforms and a lecturer mentioned that we would have to use substitution for it. I'm not asking for help with answering the question but I don't understand how you're supposed to do substitution.

Any help would be much appreciated!
Use substitution to do some of the integrals maybe?

Other than that your question is too vague.

CB

3. ## Re: Substitution when doing Laplace transforms

Yea I think so, an example of the type of question being asked is:

ℒ{t^3 e^6t}
= 3!/S^4 1/S-5

Then to get the final transformation my lecturer said to use substitution to get one single answer.

4. ## Re: Substitution when doing Laplace transforms

Is...

$\mathcal{L} \{t^{3}\ e^{6 t}\}= \int_{0}^{\infty} t^{3}\ e^{6 t}\ e^{-s\ t}\ dt$ (1)

... and using the substitution s-6= p You obtain...

$\mathcal{L} \{t^{3}\ e^{6 t}\}= \int_{0}^{\infty} t^{3}\ e^{-pt}\ dt= \frac{3!}{p^{4}} = \frac{3!}{(s-6)^{4}}$ (2)

Kind regards

$\chi$ $\sigma$

5. ## Re: Substitution when doing Laplace transforms

what I dont understand about it is where you have gotten s-6=p?

6. ## Re: Substitution when doing Laplace transforms

Originally Posted by uhm
$e^{6t}e^{-st}=e^{(6-s)t}=e^pt$