i
Applytransformrule:ifL{f(t)}=F(s)thenL{eatf(t)}=F(s−a)Fore−tsinh(3t):f(t)=sinh(3t),a=−1=L{sinh(3t)}(s+1)=s2−93=(s+1)2−93
ii
UseLaplaceTransformtable:L{tkf(t)}=(−1)kdskdk(L{f(t)})Fort9e5t:f(t)=e5t,k=9=(−1)9ds9d9(L{e5t})L(e5t)=s−51ds9d9(s−51)=−(s−5)10362880=(−1)9(−(s−5)10362880)=(s−5)10362880
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