Find the inverse Laplace Transform: $$\mathcal L^{-1} \left\lbrace 1\over s^4\right\rbrace$$
My attempt: I used the equation: $$\mathcal L\left\lbrace t^n\right\rbrace={n!\over s^{n+1}}$$
and played with some numbers until I got an answer that worked when I used the above equation. This is what I did to solve the problem and I don't know if it is the proper way to solve it. If it's not, could someone help me solve it using the "right" method?
$${\frac 16}t^3= {\frac 16}\left(3!\over s^{3+1}\right)={\frac 16}\left(6\over s^4\right)={1\over s^4}$$
Is working backwards a safe way to solve these problems or could it sometimes lead me in the wrong direction?
If you apply the Mellin's inverse formula you can use the residue theorem and then you have the right result.