Q:

inverse of laplace transform

How to compute this inverse Laplace transform ?
$$\displaystyle{ \mathcal{L^{-1}} \left\{  \frac{1}{s(\exp(s)+1)} \right\} }$$
Thanks.

A:

Google the Square wave function $\mathbf{sqw}(x)=(-1)^{\mathbf{floor}(x)}$ to find out it is a periodic function which is obviously piecewise and by using the L.T. rules we can see that $$\mathcal{L}\{\mathbf{sqw}(x)\}=\frac{1}{s}\tanh(s/2)=\frac{e^s-1}{s(e^s+1)}$$ So since $$\mathcal{L}\{1\}=\frac{1}{s}$$ I think you can do the rest.

