Find the Laplace transforms of the following functions, using the information in Table 3.1. (However, some of the individual terms in these functions may not have Laplace transforms.)

(a) f(t) = 5 + e^ˆ’3t + te^ˆ’4t

(b) f(t) = sin(4t) + t ˆ’ 3 + e^{ˆ’(tˆ’3)} + 5/t
(c) f(t) = t cos(4t) + t/5
(d) f(t) = (tˆ’1) cos(4(tˆ’1)) + t²

Table 3.1 Laplace Transforms for Various Time-Domain Functions* F(s) f() 1. 6(1) (unit impulse) 2. S(t) (unit step) 3. t (ramp) ( - 1)! 4. pi-1 5. e-br s+b 6. -et TS + 1 "-le-bt 7. ( 1)! (n > 0) (s + by 1 -m-le/t 8. T"( 1)! (ts + 1)" -(e-bt e-bit) 9. b, b2 (s + b, )(s + b2) 1 (e/i - e/2) 10. (t,s + 1)(t,8 + 1) b3- b2b! b, b, b3- b1 s+b3 (s + b, )(s+ b,) -bit 11. b, b, 12. 1, -13-1/1 + T38 +1 (t,5 + 1)(t,8 + 1) 13. 1 e-tk s(Ts + 1) 14. sin ot s2 + o? 15. cos ot s2 + o? O cos o +s sin o 16. sin(@t + 4) s2 + m? 17. e-b' sin ot } b,o real (s + b)2 + @? 18. e-bt sin ot s+b (s + b)? + o? 19. e-W/* sin(V1- ?t/t) T2s2 + 2(ts +1 (0 < ISI < 1) 1 20. 1+ -(t,e~/ti t,e-l/*3) s(T,s + 1)(T,5 + 1) (T, # T,) 21. 1 -u/t sin[ /1-?t/r+ w] V1-? s(r?s + 2ts + 1) V1-? Y = tan- (0 < I3I < 1)