# Question 2. Find the inverse Laplace transform of the given function. a) $$\mathcal{L}^{-1}\left\{\frac{1}{s^{2}}-\frac{3}{s}+\frac{1}{s+2}\right\}$$, b) $$\mathcal{L}^{-1}\left\{\frac{1}{4 s^{2}+1}\right\}$$ c) $$\mathcal{L}^{-1}\left\{\left(\frac{2}{s}+\frac{1}{s^{3}}\right)^{2}\right\}$$ d) $$\mathcal{L}^{-1}\left\{\frac{1}{s(s-1)\left(s^{2}+6 s+13\right)}\right\}$$ e) $$\mathcal{L}^{-1}\left\{\frac{s}{(s+3)\left(s^{2}+4\right)}\right\}$$, f) $$\mathcal{L}^{-1}\left\{\frac{s+1}{s^{2}-4 s}\right\}$$

Transcribed Image Text: 2. Find the inverse Laplace transform of the given function. a) $$\mathcal{L}^{-1}\left\{\frac{1}{s^{2}}-\frac{3}{s}+\frac{1}{s+2}\right\}$$, b) $$\mathcal{L}^{-1}\left\{\frac{1}{4 s^{2}+1}\right\}$$ c) $$\mathcal{L}^{-1}\left\{\left(\frac{2}{s}+\frac{1}{s^{3}}\right)^{2}\right\}$$ d) $$\mathcal{L}^{-1}\left\{\frac{1}{s(s-1)\left(s^{2}+6 s+13\right)}\right\}$$ e) $$\mathcal{L}^{-1}\left\{\frac{s}{(s+3)\left(s^{2}+4\right)}\right\}$$, f) $$\mathcal{L}^{-1}\left\{\frac{s+1}{s^{2}-4 s}\right\}$$
Transcribed Image Text: 2. Find the inverse Laplace transform of the given function. a) $$\mathcal{L}^{-1}\left\{\frac{1}{s^{2}}-\frac{3}{s}+\frac{1}{s+2}\right\}$$, b) $$\mathcal{L}^{-1}\left\{\frac{1}{4 s^{2}+1}\right\}$$ c) $$\mathcal{L}^{-1}\left\{\left(\frac{2}{s}+\frac{1}{s^{3}}\right)^{2}\right\}$$ d) $$\mathcal{L}^{-1}\left\{\frac{1}{s(s-1)\left(s^{2}+6 s+13\right)}\right\}$$ e) $$\mathcal{L}^{-1}\left\{\frac{s}{(s+3)\left(s^{2}+4\right)}\right\}$$, f) $$\mathcal{L}^{-1}\left\{\frac{s+1}{s^{2}-4 s}\right\}$$