The Hankel Transform is not a type of integral transform used in Operational Calculus. It is used in other areas of mathematics and physics, such as the study of Bessel functions.

The Laplace transform of $e^{at}$ is $\frac{1}{s-a}$.

The inverse Laplace transform of $\frac{1}{s^2+a^2}$ is $\frac{1}{a}\sin(at)$.

The Differentiation Property of the Laplace transform states that $L{f'(t)}=sF(s)-f(0^+)$.

The Laplace transform of the unit step function $u(t)$ is $\frac{1}{s}$.

The convolution theorem for the Laplace transform states that $L{f(t)*g(t)}=F(s)G(s)$.

The Laplace transform of the Dirac delta function $\delta(t)$ is $1$.

The final value theorem for the Laplace transform states that $\lim_{t\to\infty}f(t)=\lim_{s\to 0}sF(s)$.

The Laplace transform of the Heaviside step function $H(t)$ is $\frac{1}{s+1}$.

The initial value theorem for the Laplace transform states that $\lim_{t\to 0^+}f(t)=\lim_{s\to\infty}sF(s)$.

The Laplace transform of the exponential function $e^{-at}$ is $\frac{1}{s+a}$.

The Integration Property of the Laplace transform states that $L{\int_0^t f(\tau)d\tau}=\frac{F(s)}{s}$.

The Laplace transform of the cosine function $\cos(at)$ is $\frac{s}{s^2+a^2}$.

The shifting theorem for the Laplace transform states that $L{f(t-a)u(t-a)}=e^{-as}F(s)$.