Find the \(L^{-1} (\frac{s}{(s-1)^7})\).

1.	Find the \(L^{-1} (\frac{s}{(s-1)^7})\).
A.	\(e^{-t} \left (\frac{t^6}{5!}+\frac{t^5}{6!}\right )\)
B.	\(e^t \left (\frac{t^6}{5!}+\frac{t^5}{6!}\right )\)
C.	\(e^t \left (\frac{t^6}{6!}+\frac{t^5}{5!}\right )\)
D.	\(e^{-t} \left (\frac{t^6}{6!}+\frac{t^5}{5!}\right )\)
Answer» D. \(e^{-t} \left (\frac{t^6}{6!}+\frac{t^5}{5!}\right )\)

Discussion

The \(L^{-1} \left (\frac{3s+8}{s^2+4s+25}\right )\) is \(e^{-st} (3cos⁡(\sqrt{21}t+\frac{2sin⁡(\sqrt{21}t)}{\sqrt{21}})\). What is the value of s?
Find the \(L^{-1} \left (\frac{s}{(s^2+1)(s^2+2)(s^2+3)}\right )\).
Find the \(L^{-1} (\frac{1}{(s^2+4)(s^2+9)})\).
Find the \(L^{-1} \left (\frac{(3s+9)}{(s+1)(s-1)(s-2)}\right )\).
Find the \(L^{-1} (\frac{s}{2s+9+s^2})\).
Find the \(L^{-1} (\frac{s}{(s-1)^7})\).
Find the \(L^{-1} (\frac{1}{(s+2)^4})\).
Find the \(L^{-1} (\frac{s+3}{4s^2+9})\).