Laplace transformation of a function?

Question

(t^3)/24 -3t + 2

I need some steps that show me how to solve this type of question. Thanks

Answer 1

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Note that

L{t^n} = n! / s^(n+1).

So,

L{(t^3)/24 -3t + 2}

= (1/24) L{t^3} - 3 L{t} + 2 L{1}

= (1/24) (3!/t^4) - 3(1/s^2) + 2 (1/s)

= t^4/4 - 3/s^2 + 2/s.

I hope this helps!

Answer 2

Y(s) = Integral of {e^(-st) * [t^3/24 - 3t + 2] dt

Treat "s" as a constant. Integrate from 0 to infinity. If you need help to integrate the Laplace transform, consider using integration by parts.