Find the (L^{-1} left ( frac{(s+1)}{(s+2)(s+3)} 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 ) ).
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} 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}) ).