#	$$f(t) = \mathcal{L}^{-1}\{F(s)\}$$	$$F(s) = \mathcal{L}\{f(t)\}$$
1	$$1$$	$$\frac{1}{s}, \quad s > 0$$
2	$$e^{at}$$	$$\frac{1}{s-a}, \quad s > a$$
3	$$t^n, \quad n = 1, 2, 3, \dots$$	$$\frac{n!}{s^{n+1}}, \quad s > 0$$
4	$$t^p, \quad p > -1$$	$$\frac{\Gamma(p+1)}{s^{p+1}}, \quad s > 0$$
5	$$\sin(at)$$	$$\frac{a}{s^2+a^2}, \quad s > 0$$
6	$$\cos(at)$$	$$\frac{s}{s^2+a^2}, \quad s > 0$$
7	$$\sinh(at)$$	$$\frac{a}{s^2-a^2}, \quad s > |a|$$
8	$$\cosh(at)$$	$$\frac{s}{s^2-a^2}, \quad s > |a|$$
9	$$e^{at}\sin(bt)$$	$$\frac{b}{(s-a)^2+b^2}, \quad s > a$$
10	$$e^{at}\cos(bt)$$	$$\frac{s-a}{(s-a)^2+b^2}, \quad s > a$$
11	$$t^n e^{at}$$	$$\frac{n!}{(s-a)^{n+1}}, \quad s > a$$
12	$$u_c(t)$$	$$\frac{e^{-cs}}{s}, \quad s > 0$$
13	$$u_c(t)f(t-c)$$	$$e^{-cs}F(s)$$
14	$$e^{ct}f(t)$$	$$F(s-c)$$
15	$$f(ct)$$	$$\frac{1}{c}F\left(\frac{s}{c}\right), \quad c > 0$$
16	$$\int_0^t f(t-\tau)g(\tau) d\tau$$	$$F(s)G(s)$$
17	$$\delta(t-c)$$	$$e^{-cs}, \quad s > 0$$
18	$$f^{(n)}(t)$$	$$s^n F(s) - s^{n-1}f(0) - \dots - f^{(n-1)}(0)$$
19	$$(-t)^n f(t)$$	$$F^{(n)}(s)$$