# Find the Laplace transform of $$\displaystyle{f{{\left({t}\right)}}}={10}{t}{e}^{{-{5}{t}}}$$

Find the Laplace transform of $f\left(t\right)=10t{e}^{-5t}$
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stecchiniror7
We have:
$\mathcal{L}\left(t\right)=\frac{1}{{s}^{2}}$
Thus, we have:
$\mathcal{L}\left(10t{e}^{-5t}\right)=10F\left(s+5\right)=\frac{10}{{\left(s+5\right)}^{2}}$
Note: we made use of the Shifting Theorem, which was mentioned to you in another post.
###### Not exactly what you’re looking for?
granfury90210birm
HINT:
Use

and
$L\left({t}^{n}\right)=\frac{\mathrm{\Gamma }\left(n+1\right)}{{s}^{n+1}}$
and
$\mathrm{\Gamma }\left(n+1\right)=n!$ if n is non-negative integer