Use the "Table of Laplace transforms" to find the Laplace transform of the function. A preliminary integration by parts may be necessary.
$\displaystyle f(t)=te^t$
Use the "Table of Laplace transforms" to find the Laplace transform of the function. A preliminary integration by parts may be necessary.
$\displaystyle f(t)=te^t$
In this particular case if $\displaystyle \mathcad{L} \{f(t)\} = F(s)$, then $\displaystyle \mathcad{L} \{t\ f(t)\} = - \frac{d}{d s} F(s)$. The more general case $\displaystyle \mathcad{L} \{f(t)\ g(t)\}$ requires the solution of an integral in the complex plane...
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$\displaystyle \chi$ $\displaystyle \sigma$