(*  \(Try\ the\ examples\ below\ by\ \((1)\)\ loading\ the\ package\ 
          Calculus`LaplaceTransform`\ only

        	\ \ \ \ \((2)\)\ loading\ the\ package\ MoreInvLaplace.m\)		 *)




<< Calculus`LaplaceTransform`

\(\(<< MoreInvLaplace.m

\)\)

(*  Bessel functions examples. *)

InverseLaplaceTransform[BesselK[0, (Sqrt[a s])], s, t]

\(\(

InverseLaplaceTransform[BesselK[0, a\ s], s, t]\)\)

InverseLaplaceTransform[BesselK[0, a s]/s, s, t]

\(\(

InverseLaplaceTransform[s\ \ BesselK[0, 2\ s], s, t]\)\)

\(\(
InverseLaplaceTransform[\ BesselK[1, s], s, t]\)\)

\(\(


InverseLaplaceTransform[\ BesselK[1, s]/s\^3, s, t]\)\)

\(\(

InverseLaplaceTransform[\ BesselK[5, s], s, t]\)\)

(* Hyperbolic functions examples. *)

\(\(
InverseLaplaceTransform[\ Cosh[a\/s], s, t]\)\)

\(\(

InverseLaplaceTransform[\ Cosh[a\/s]\/\@s, s, t]

\)\)

\(\(


InverseLaplaceTransform[\ Cosh[a\/s]\/\(s \@ s\), s, t]
\)\)

\(\(
InverseLaplaceTransform[\ Sinh[a\/s], s, t]\)\)

\(\(

InverseLaplaceTransform[\ Sinh[2\/s]\/\@s, s, t]

\)\)

\(\(


InverseLaplaceTransform[\ Sinh[π\/s]\/\(s \@ s\), s, t]

    \)\)

(* Miscellaneous examples. *)

\(\(


    InverseLaplaceTransform[\(s \@\( s + 1\)\)\/\(s\^3 + s\^2 + s + 1\), s, t]
      
\)\)

\(\(

InverseLaplaceTransform[\(s\ Log[s]\)\/\(s\^2 + 1\), s, t]
\)\)

\(\(


    InverseLaplaceTransform[\(s\ Log[π\ s]\)\/\(s\^2 + 1\), s, t]\)\)

\(\(

InverseLaplaceTransform[Exp[s]\/\(s \((Exp[s] + 1)\)\), s, t]

    \)\)

\(\(


    InverseLaplaceTransform[Exp[2  s]\/\(s \((Exp[2  s] + 1)\)\), s, t]\)\)

\(\(


Plot[RectangularWave[1, t], {t, 0, 3}]\)\)

\(\(

Plot[RectangularWave[2, t], {t, 0, 6}]\)\)

LaplaceTransform[(∫_0^t) f[t] \[DifferentialD]t, t, s]