Laplace transform of Hyperbolic Sin(at)

the Laplace transform, named after its inventor Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable {\displaystyle t} (often time) to a function of a complex variable {\displaystyle s} (complex frequency). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms linear differential equations into algebraic equations and convolution into multiplication.
#math
#integration
#Laplace transform