Question

Use the definition of the Laplace transform to find L(f(t) if f(t)=t^5

Answer 1

`\mathcal{L}\{t^n\}=(n!)/(s^(n+1))`

So

`\mathcal{L}\{f(t)\}=(5!)/(s^(5+1))=(120)/(s^6)`

Answer 2

120/s^6

Explanation:

There is an easy formula for this...

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

Your n=5 here

L(t^5)=5!/(s^6)

L(t^5)=120/s^6