<< Calculus`LaplaceTransform`

LaplaceTransform[t^6  Cos[4  t], t, s]

\(\(
LaplaceTransform[DiracDelta[t - 5] f[t], t, s]\)\)

InverseLaplaceTransform[3 + E^(-2 s)/s + 1/(s^3 + 1), s, t]

\(\(
Apart[\((s^3 + 5  s)\)/\((s^3 + 2  s^2 - 5  s - 6)\)]\)\)

Apart[(x^2 + 9  x^5)/(x^3 + 2  x^2 + 2  x + 2)]