How can I solve this Laplace transformation?

Question

_{e^4t*t, my professor doesn't know how to solve this problem, and neither do I}

Answer 1

Laplace transform of function  f(t) is defined as ∫₀^∞f(t)e^-stdt. So

∫₀^∞e^4t*te^-stdt=∫₀^∞e^t(4t-s)dt.

It can be written as

(√π/4) e^{-(s^2/16)} (-i + Erfi(s/4))

where Erfi(z) is so called imaginary error function = Erf(iz)/i. 

Erf(z)=2/√π∫₀^te^{t^2}dt.
Indeed, evaluating that integral is not that easiy.