Laplace Transform/Examples/Example 1

Example of Laplace Transform
Let $\laptrans f$ denote the Laplace transform of the real function $f$.


 * $\laptrans {4 e^{5 t} + 6 t^3 - 3 \sin 4 t + 2 \cos 2 t} = \dfrac 4 {s - 5} + \dfrac {36} {s^4} - \dfrac {12} {s^2 + 16} + \dfrac {2 s} {s^2 + 4}$