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關於拉氏轉換的問題
G(s)=2(s+1)/(s(s^2+s+2)) 請問如何拉氏轉換 部分積分卡住了 求詳解<div></div> http://latex.codecogs.com/gif.latex?\begin{align*}%20G(s)&=\frac{2(s+1)}{s(s^2+s+2)}\\&=\frac{1-s}{s^2+s+2}+\frac{1}{s}\\&=\frac{1}{s}-\frac{s+\frac{1}{2}}{(s+\frac{1}{2})^2+\frac{7}{4}}+\frac{\frac{3\sqrt7}{2}}{\sqrt7((s+\frac{1}{2})^2+\frac{7}{4})}\end{align*}\\$since%20,%20$\\%20\begin{align*}%20L^{-1}\left(%20\frac{2(s+1)}{s(s^2+s+2)}\right%20)&=L^{-1}\left(%20\frac{1}{s}\right%20)-L^{-1}\left(\frac{s+\frac{1}{2}}{(s+\frac{1}{2})^2+\frac{7}{4}}%20\right%20)+\frac{3}{\sqrt7}L^{-1}\left(%20\frac{\frac{\sqrt7}{2}}{(s+\frac{1}{2})^2+\frac{7}{4}}\right%20)\\&=1-e^{-t/2}\cos\left(\frac{\sqrt7}{2}t%20\right%20)+\frac{3}{\sqrt7}e^{-t/2}\sin\left(\frac{\sqrt7}{2}t%20\right%20)\end{align*}
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