# Find the Laplace Transform of L{(sin ht)/t}

Find the Laplace Transform of $L\left\{\left(\mathrm{sin}ht\right)/t\right\}$
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Jaylynn Huffman
Given that $L\frac{\mathrm{sin}ht}{t}$
we know that $Lf\left(t\right)=\overline{f}\left(s\right).ThenL\frac{1}{t}f\left(t\right)={\int }_{s}^{\mathrm{\infty }}\overline{f}\left(s\right)ds$
$L\mathrm{sin}ht=\frac{1}{{s}^{2}-1}$
$L\frac{1}{t}\mathrm{sin}ht={\int }_{s}^{\mathrm{\infty }}\frac{1}{{s}^{2}-1}ds$
$=\left[\frac{1}{2}\mathrm{log}|\frac{s-1}{s+1}|{\right]}_{s}^{\mathrm{\infty }}$