How do I find it? The Laplace transform of L(te^t cos t)

The Laplace transform of $\mathcal{L}\left(t{e}^{t}\mathrm{cos}t\right)$
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$\mathcal{L}\left(tcost\right)=-\frac{d}{ds}\left(\frac{s}{{s}^{2}+1}\right)=\frac{{s}^{2}-1}{\left({s}^{2}+1{\right)}^{2}}$
$\text{so the final answer is:}$
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Annie French
You need the relation
$\mathcal{L}\left\{tf\left(t\right)\right\}⟺-{F}^{\prime }\left(s\right)$
i.e. multiplication in the time domain corresponds to differentiation in the s-domain (and a negative sign). Since you know F(s), you can easily derive the result.
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