Question
Evaluate the Laplace transform of the given function using appropriate theorems and examples from this section.$$f(t)=t^{4} e^{-3 t}+e^{t}$$
Step 1
1) For the first term, we can use the Laplace transform of $t^n e^{-at}$, which is given by: $$ \mathcal{L}\{t^n e^{-at}\} = \frac{n!}{(s+a)^{n+1}} $$ In our case, $n = 4$ and $a = 3$. So, the Laplace transform of the first term is: Show more…
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