무제

1844 days 전, rksekwnwls@gmail.com 작성

int _{} ^{} {{ds} over {s ^{2} (s-1) ^{2}}}# # {1} over {s ^{2} (s-1) ^{2}}# = {a} over {s} + {b} over {s ^{2}} + {c} over {s-1} + {d} over {(s-1) ^{2}}# = {as(s-1) ^{2} +b(s-1) ^{2} +cs(s-1)+ds ^{2}} over {s ^{2} (s-1) ^{2}}# = {a(s ^{3} -2s+s)+b(s ^{2} -2s+1)+c(s ^{3} -s ^{2} )+ds ^{2}} over {s ^{2} (s-1) ^{2}}# = {(a+c)s ^{3} +(-2a+b-c+d)s ^{2} +(a-2b)s+b} over {s ^{2} (s-1) ^{2}}# # a+c=0 CDOTS ➀# -2a+b-c+d=0 CDOTS ➁# a-2b=0 CDOTS ➂# b=1 CDOTS ➃# # a=2( BECAUSE ➂,➃)``# c=-2( BECAUSE ➀,➂,`➃)# d=1(` BECAUSE `➀,➁,➂,➃)# # {1} over {s ^{2} (s-1) ^{2}}# = {2} over {s} + {1} over {s ^{2}} + {-2} over {s-1} + {1} over {(s-1) ^{2}}# # int _{} ^{} {{ds} over {s ^{2} (s-1) ^{2}}}# = int _{} ^{} {{2} over {s} + {1} over {s ^{2}} + {-2} over {s-1}+{1} over {(s-1)} ^{2}}# = 2ln|s| - {1} over {s} -2ln|s-1| - {1} over {s-1} + C