Question

What is the Laplace Transform of:

f(t)=6e^(−5t)+e^(3t)+5t^3−9

Answer 1

`\boxed{ℒ_t[f(t)] =\frac{30}{{s}^(4) } - (9)/(s) + (6)/(s + 5) + (1)/(s - 3)}`

This holds true because:

`\lim_(s\to\infty) [\frac{30}{{s}^(4) } - (9)/(s) + (6)/(s + 5) + (1)/(s - 3)] =0`

[The answer is throughly verified, hence you can trust this :)]