Chapter 7.1, Problem 22P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform of the given function $f\left(t\right)={\sinh }^{2}3t$ .

Summary introduction:Program will use the definition of Laplace transform of function $F\left(s\right)$ for all $t\ge 0$ and is defined as,

  $L\left\{f\left(t\right)\right\}={\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-st}f\left(t\right)dt}$ …… (1)

Here, the improper integral will converges for all values of $s$ .