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Given that

$\mathcal{L}[f(t)]=\frac{s+2}{s^2+1}, \mathcal{L}[f(t)]=\frac{s^2+1}{(s+3)(s+2)}, $ 

$h(t)=\int_0^1 f(\tau) g(t-\tau) d \tau, \mathcal{L}[h(t)]$ is

  1. $\frac{s^2+1}{s+3}$
  2. $\frac{1}{s+3}$
  3. $\frac{s^2+1}{(s+3)(s+2)}+\frac{s+2}{s^2+1}$
  4. None of these
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