laplace(f(t))

syms s t a b w

laplace(a)
laplace(t^2)
laplace(t^9)
laplace(exp(-b*t))
laplace(sin(w*t))
laplace(cos(w*t))

ans =
   1/s^2

ans =
   2/s^3

ans =
   362880/s^10

ans =
   1/(b + s)

ans =
   w/(s^2 + w^2)

ans =
   s/(s^2 + w^2)

ilaplace(1/s^3)

ans =
   t^2/2

syms s t a b w

ilaplace(1/s^7)
ilaplace(2/(w+s))
ilaplace(s/(s^2+4))
ilaplace(exp(-b*t))
ilaplace(w/(s^2 + w^2))
ilaplace(s/(s^2 + w^2))

ans =
   t^6/720

ans =
   2*exp(-t*w)

ans =
   cos(2*t)

ans =
   ilaplace(exp(-b*t), t, x)

ans =
   sin(t*w)

ans =
   cos(t*w)

syms x 
f = exp(-2*x^2);     %our function
ezplot(f,[-2,2])     % plot of our function
FT = fourier(f)      % Fourier transform

FT =
   (2^(1/2)*pi^(1/2)*exp(-w^2/8))/2

ezplot(FT)

f = ifourier(-2*exp(-abs(w)))

f =
   -2/(pi*(x^2 + 1))