Laplace Transform of f(t) = t^2 e^{2t} cos(3t)

ODEs (Requires Complex Numbers): Find the Laplace transform of the function f(t) = t^2 e^{2t} cos(3t). We give a heuristic method that combines the First Shift Formula and Euler's formula with the rule for L(t^n). This method applies in general to f(t) = t^n e^{at} cos(bt) and g(t) = t^n e^{at} sin(bt).

[HariPrezadu]

Thank you so much I am writing my series exam with this

[MathDoctorBob]

@flynt000099 Thanks! I'm happy to add more Laplace transform videos if you need them. - Bob

[dannyjason]

Thank you so much.. but what about sin ? how do you take the imaginary part instead of the real part ?

[NamelessProducts]

Thank you so much. I really can't thank you enough.

[coloring-home-board]

thank you
what is the Laplace transform f(t)=2e^-t cos10t - t^4 + 6e^-(t-10), t<1

[henriberger]

In warmup 2, does the shift from cos(3t) to e^(i3t) work for sin as well?

[MathDoctorBob]

Yes. Just take the imaginary part instead.

[Edutechplus.]

plz help..

show me laplce tranform of (t+2)^2.e^t

[TheoMarpena]

U need to improve more on how you explain