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      $$\begin{array}{cc}
      f(t)&F(s)\\
      \hline
      \frac{1}{2\pi i}\int_{s'-i\infty}^{s'+i\infty}F(s)e^{st}ds&\int_0^\infty f(t)e^{-st}dt\\
      \delta(t)&1(s)\\
      u(t)&\frac{1}{s}\\
      t&\frac{1}{s^2}\\
      t^n&\frac{n!}{s^{n+1}}\\
      \begin{pmatrix}\sin&\cos\\\sinh&\cosh\end{pmatrix}(\omega t)&\frac{\begin{pmatrix}\omega&s\end{pmatrix}}{s^2\pm \omega^2}\\
      u(t-a)f(t-a)&e^{-as}F(s)\\
      e^{at}f(t)&F(s-a)\\
      (f\star g)(t)=\int_0^t f(t-\tau)g(\tau)d\tau&F(s)G(s)\\
      f'(t)&sF(s)-f(0)\\
      f^{(n)}(t)&s^nF(s)-s^\downarrow f^{(\uparrow)}(0)\\
      \end{array}$$
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    <a href="https://tutorial.math.lamar.edu/classes/de/laplace_table.aspx">Paul's Laplace Transforms</a>
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