this problem has been giving me a bit of trouble and was posting it to here to help me get some clarification. I know that I have to complete the square, but I end up getting lost at that point. Any help is much appreciated!

$$L^{-1} \big\{\frac{s}{s^2+6s+10}\big\}$$


$$F(s) = \frac{s}{s^2+6s+10}$$

$$ \frac{s+3-3}{(s+3)^2+1} = \frac{s+3}{(s+3)^2+1} - \frac{3}{(s+3)^2+1}$$

$$f(t) = L^{-1} \{F(s)\} = e^{-3t} \cos t - 3e^{-3t} \sin t$$

  • $\begingroup$ Thank you very much for walking me through it. $\endgroup$ – J. Armstrong Nov 14 '17 at 14:31
  • $\begingroup$ @J.Armstrong: my pleasure. Once you receive complete answers in MSE, it is better to accept the best one and close the question. $\endgroup$ – Amin Nov 14 '17 at 14:33

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