In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t).

f (t) = te^-t sin² t

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THEOREM 2 Differentiation of Transforms If f(t) is piecewise continuous for t≥ 0 and f(t)| ≤ Mect as t→ +∞o, then L{-tf(t)} = F' (s) for sc. Equivalently, f(1) = £¯'{F(s)} = —-—-L¯' {F'(s)}. Repeated application of Eq. (6) gives for n 1, 2, 3, .... = L{t" f(t)} = (-1)"F(n) (s) (6) (7) (8)