# Find Laplace transform Lleft{(t-3)^2u(t-3)right}

Find Laplace transform
$L\left\{\left(t-3{\right)}^{2}u\left(t-3\right)\right\}$
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Step 1
We can use following concepts to find laplace transform of given function:
Concept

Step 2
$t\left[{t}^{n}\right]=\frac{\left(n!\right)}{{s}^{n+1}}$
we have to find
$L\left[\left(t-3{\right)}^{2}u\left(t-3\right)\right]$
$⇒L\left[{t}^{2}\right]=\frac{2!}{{s}^{2+1}}$
$⇒L\left[{t}^{2}\right]=\frac{2}{{s}^{3}}$

Hence $L\left[\left(t-3{\right)}^{2}u\left(t-3\right)\right]={e}^{-3s}\cdot \frac{2}{{s}^{3}}$