Question

the Laplace transforms of e^-5t​

Answer 1

Answer:

As we all know that,

L { f(t) } = F(s)

L { t*f(t) } = -d( F(s) )/dt

f(t) = e^-5t then Laplace transform is F(s) = 1/(s+5)

t*f(t) = t*e^-5t then the Laplace transform is -d{ 1/(s+5) }/dt

L { t*f(t) } = 1/(s+5)².