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+1}{(s-1)(s+2)^2} right ) ).
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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} left ( frac{(s+1)}{(s+2)(s+3)} 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}) ).