Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - Problems - Page 694: 23

$L[ e^t-te^{-2t}]=\dfrac{1}{(s-1)}-\dfrac{1}{(s+2)^2}$

The Laplace transform of function $t^3$ is given as: $L(e^t)=\dfrac{1}{s-1}$ and $L(t)=\dfrac{1}{s^2}$ The first shifting Theorem for $a=- 2$ can be expressed as: $L[ e^t-te^{-2t}]=\dfrac{1}{(s-1)}-\dfrac{1}{(s+2)^2}$