# L{t-3^(-3t)} which of the laplace transform is 1) L{t-3^(-3t)}=1/s^2+1/(s-3) 2) L{t-3^(-3t)}=1/s^2-1/(s-3)

$L\left\{t-{e}^{-3t}\right\}$
which of the laplace transform is

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Step 1
We know the Laplace transforms $L\left\{{t}^{n}\right\}=\frac{n!}{{s}^{n+1}},s>0$
$L\left\{{e}^{at}\right\}=\frac{1}{\left(s-a\right)},s>0$

$L\left\{t\right\}=\frac{1}{{s}^{2}},s>0$
$L\left\{t-{e}^{-3t}\right\}=-\frac{1}{s+3},s>-3$
$L\left\{t-{e}^{-3t}\right\}=\frac{1}{{s}^{2}}-\frac{1}{\left(s+3\right)}$
Step 2
Answer: $L\left\{t-{e}^{-3t}\right\}=\frac{1}{{s}^{2}}-\frac{1}{s+3}$ option 4) is correct