Tabla básica de transformadas de Laplace

$$f(t) \ \ (t>0) $$ $$F(s)={\cal L}[f]$$

$$1$$ $$\frac{1}{s}\ \ ,\ \ \ s>0$$

$$e^{at}$$ $$\frac{1}{s-a}\ \ ,\ \ \ s>a$$

$$t^n\ \ ,\ \ \ n \ \mbox{natural}$$ $$\frac{n!}{s^{n+1}}\ \ ,\ \ \ s>0$$

$$\mbox{sen}\, at$$ $$\frac{a}{s^2+a^2}\ \ ,\ \ \ s>0$$

$$\cos at$$ $$\frac{s}{s^2+a^2}\ \ ,\ \ \ s>0$$

$$\sqrt{t}$$ $$\frac{\sqrt{\pi}}{2}s^{-3/2}\ \ ,\ \ \ s>0$$

$$\frac{1}{\sqrt{t}}$$ $$\sqrt{\pi}s^{-1/2}\ \ ,\ \ \ s>0$$

$$f(t) \ \ (t>0) $$	$$F(s)={\cal L}[f]$$
$$1$$	$$\frac{1}{s}\ \ ,\ \ \ s>0$$
$$e^{at}$$	$$\frac{1}{s-a}\ \ ,\ \ \ s>a$$
$$t^n\ \ ,\ \ \ n \ \mbox{natural}$$	$$\frac{n!}{s^{n+1}}\ \ ,\ \ \ s>0$$
$$\mbox{sen}\, at$$	$$\frac{a}{s^2+a^2}\ \ ,\ \ \ s>0$$
$$\cos at$$	$$\frac{s}{s^2+a^2}\ \ ,\ \ \ s>0$$
$$\sqrt{t}$$	$$\frac{\sqrt{\pi}}{2}s^{-3/2}\ \ ,\ \ \ s>0$$
$$\frac{1}{\sqrt{t}}$$	$$\sqrt{\pi}s^{-1/2}\ \ ,\ \ \ s>0$$