Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.2 The Existence of the Laplace Transform and the Inverse Transform - True-False Review - Page 685: h

False

We must know that the Laplace transform of a periodic function can never be periodic. This implies that the given function $\dfrac{1}{(s^2+1)(1-e^{-\pi s})}$ represents a decreasing function, thus it cannot be considered as a periodic function. Therefore, the given statement is $\bf{False}$.