Solution 2.9.3.4
F(s) =
Z
1
0
sinh(t)e
;st
dt =
Z
1
0
e
t
;e
;t
2
e
;st
dt
=
Z
1
0
e
;(s;1)t
2
dt;
Z
1
0
e
;(s+1)t
2
dt
=
;1
2(s;1)
h
e
;(s;1)t
i
1
0
;
;1
2(s+1)
h
e
;(s+1)t
i
1
0
=
1
2(s;1)
;
1
2(s +1)
;; Re (s) > 1;;
=
1
(s;1)(s+1)
;; Re (s) > 1;;
1