In Fourier transform we shift from time domain to frequency domain through a general formula but intuition behind this formula lies in translating the signal to another plane and then aiming for center of mass and the formula of average came from there
Reference https://youtu.be/spUNpyF58BY (An amazing video by 3b1b explaining fourier transform)
In Laplace transform we shift from time domain to complex s domain of course a formula exist but i want to know how this formula comes up . In other words, what was in mind of Laplace when he was somehow deriving this formula 
How come integrating in time domain equal to dividing by s and derivating means multiplication by s . Similarly exponentiating in time domain is equal shifting in s domain .
