LaPlace Table

1

1/s

e^at

1/(s-a)

tⁿe^at

n!/(s-a)ⁿ⁺¹

e^atcos(bt)

(s-a)/(s-a)²+b²

e^atsin(bt)

b/(s-a)²+b²

tⁿf(t)

(-1)ⁿ * (d/ds)ⁿF(s)

∫(0,t)f(x)g(t-τ)dτ

F(s)G(s)

tⁿ (n = 0, 1, 2…)

n!/(sⁿ⁺¹)

e^atf(t)

F(s-a)

u_a(t)

e^-as/s

f(t-a)*u_a(t)

e^-asF(s)

δ_a(t)

e^-as

fⁿ(t)

sⁿF(s)-s^(n-1)f(0)-…-f^(n-1)(0)