How to show step-by-step solutions for Laplace transforms?

Questions
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1

Hello,

I tried to compute Laplace transform(sin(3t-2)*e^(-2t)) using WolframAlpha and I see no step-by-step solution. I hope anyone could guide me on a way to show step-by-step solutions for solving Laplace tranforms. I am using WolframAplha Pro.

Thank you.

2

What kind of step-by-step solution would be useful to you in this case? Would you want to see a solution that made use of a table of Laplace transforms?

Step-by-Step solutions for Laplace transforms doesn’t seem to be implemented. You may be able to get a solution by typing the corresponding integral into WolframAlpha.

3

I have special access code that I use to get step-by-step solution :slight_smile: Here is the solution, step by step:

8056Drawing1.png
8056Drawing1.png922×1577 93.5 KB

Check with Mathematica:

LaplaceTransform[Sin[3 t - 2]*E^(-2 t), t, s]

6197Untitled.png

4

I just tried what Sean recommended and it worked OK. Not as detailed as Nasser, but that just computes a tble integral. First you put in W|A fully defined Laplace integral

int sin(3*t-2)*e^(-2*t-s*t) from 0 to inf

and then click “show steps”.

ScreenShot2013-11-27at9.05.43PM.png
ScreenShot2013-11-27at9.05.43PM.png600×421 70.6 KB

WolframAlpha--int_sin_3_t_2__e___2_t_s_t__from_0_to_inf___Indefinite_integral__2013_11_27_2059.gif
WolframAlpha--int_sin_3_t_2__e___2_t_s_t__from_0_to_inf___Indefinite_integral__2013_11_27_2059.gif478×571 14.3 KB

5

Hi Nasser,

Can you please advice how did you obtain the special access for getting Laplace transform steps?

Thanks

6

Can you please advice how did you obtain the special access for
getting Laplace transform steps

I do not have special access, that was a joke (notice the smiley). I wrote the above myself. I think the best you can get now with an automated step by step is Sam’s answer below using Wolfram Alpha.