#maths
| transform | result |
| --- | --- |
| $\mathcal L [0]$ | 0 | 
| $\mathcal L [1]$ | $\frac{1}{s}$|
| $\mathcal L [x]$ | $\frac{1}{s^2}$|
|$\mathcal L [x^2]$|$\frac{2}{s^3}$|
|$\mathcal L [x^n]$|$\frac{n!}{s^{n+1}}$ |
|$\mathcal L [\sin(ax)]$|$\frac{a}{s^2+a^2}$|
|$\mathcal L [\cos(ax)]$|$\frac{s}{s^2 + a^2}$|
|$\mathcal L [xf(x)]$|$-\frac{d\tilde f}{ds}$|