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B. Evaluate the following: \text { (b) } L\left\{\int_{0}^{t} e^{-2 r} \cos \tau d \tau\right\} \text { (c) } L^{-1}\left[\frac{e^{-2 u}(s-1)}{(s+1)^{3}}\right] \text { (d) } L^{-1}\left[e^{-3 s} \frac{s+5}{s^{2}+2 s+3}\right] \text

{ (e) Let } f(t)=2+4 u(t-1)+3 u(t-3) \text {. Sketch the graph of } f \text {, and find } its Laplace transform. L\left[e^{t-1}(t-1)^{4} u(t-1)\right]

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