Inverse Laplace Transform of $$$\frac{2 s - 1}{s^{4} + s^{2} + 1}$$$
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Your Input
Find $$$\mathcal{L}^{-1}_{s}\left(\frac{2 s - 1}{s^{4} + s^{2} + 1}\right)$$$.
Answer
The Inverse Laplace transform of $$$\frac{2 s - 1}{s^{4} + s^{2} + 1}$$$A is $$$\frac{\sqrt{3} e^{\frac{t}{2}} \sin{\left(\frac{\sqrt{3} t}{2} \right)}}{2} + \frac{e^{\frac{t}{2}} \cos{\left(\frac{\sqrt{3} t}{2} \right)}}{2} - \frac{5 \sqrt{3} e^{- \frac{t}{2}} \sin{\left(\frac{\sqrt{3} t}{2} \right)}}{6} - \frac{e^{- \frac{t}{2}} \cos{\left(\frac{\sqrt{3} t}{2} \right)}}{2}.$$$A
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