Use the transforms in Fig. 10.1.2 to find the Laplace transforms of the functions in Problems 11 through 22. A preliminary integration by parts may be necessary.

 f (t) = te^t

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t f(t) t" (n ≥0) g@ (a>−1) eat cos kt sin kt cosh kt sinhkt u(t - a) 13 S n! gn+T F(s) Γ(α + 1) sa+1 s-a S s²+k² s²+k² S s²-k² s2k² -as S (s > 0) (s > 0) (s > 0) (s > 0) (s> a) (s > 0) (s > 0) (s> |k|) (s> |k|) (s > 0) FIGURE 10.1.2. A short table of Laplace transforms.