Solution 2.9.4.2 For F(s)= 10(s+2) s 2 (s +4) Find f(t)bypartial fraction expansion. 1 Solution: invlaplace2 F(s)= A s + B s 2 + C s +4 : A =  d ds [s 2 F(s)]  s=0 = " d ds s 2 [10(s+2)] s 2 (s +4) !# s=0 =  d ds  10(s +2) (s +4)  s=0 =  ;10(s +2) (s +4) 2 + 10 (s +4)  s=0 = 5 4 B = h [s 2 F(s)] i s=0 = " s 2 [10(s+2)] s 2 (s +4) # s=0 =  10(s +2) (s +4)  s=0 = 5 C = [[(s +4)F(s)]] s=;4 =  (s +4)[10(s+2)] s 2 (s +4)  s=;4 =  10(s +2) s 2  s=;4 = ; 5 4 f(t)=[1:25+ 5t;1:25e ;4t ]1(t): 2