Question

Find Laplace transform of t^n(sin(t))

Answer 1

There is a general formula
if F[s] is the Laplace transform of f, then\[
L( t^n f(t)) = (-1)^n F^{(n)}(s)\]

Answer 2

\[
L( \sin(t)]=\frac{1}{s^2+1}\\
L( t^n \sin(t)]=(-1)^n Derivative[\frac{1}{s^2+1},\{s,n\}]
\]