# Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace tranform of the function below.

Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace tranform of the function below.
$$\displaystyle{e}^{{-{2}{t}}}{\cos{{6}}}{t}+{e}^{{{5}{t}}}-{1}$$

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Elberte

Step 1
$$L\left\{e^{-2t}\cos 6t + e^{5t}-1\right\}$$
$$L\left\{e^{at}\right\}=\frac{1}{s-a}$$
$$L\left\{\cos bt \right\}= \frac{s}{s^2+b^2}$$
$$L\left\{e^{at} \cos bt\right\} =\frac{s-a}{(s-a)^2+b^2}$$
$$\displaystyle={\frac{{{s}+{2}}}{{{\left({s}+{2}\right)}^{{2}}+{6}^{{2}}}}}+{\frac{{{1}}}{{{s}-{5}}}}-{\frac{{{1}}}{{{s}}}}$$
$$L\left\{e^{-2t}\cos 6t+e^{5t}-1\right\}=\frac{s+2}{(s+2)^2+36}+\frac{1}{s-5}-\frac{1}{s}$$