What is the Inverse Laplace Transform of Y(s) = (1/τs+1)(1/s)?

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SUMMARY

The Inverse Laplace Transform of Y(s) = (1/τs + 1)(1/s) can be computed using the properties of linearity and partial fraction decomposition. The individual transforms are L^{-1}(1/τs + 1) = (1/τ)e^{-t/τ} and L^{-1}(1/s) = 1. By factoring τ out of the denominator and applying partial fraction expansion, Y(s) can be expressed as a sum of simpler fractions, facilitating the calculation of the inverse transform.

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Homework Statement


Take the Inverse Laplace Transform of: Y(s)=\frac{1}{\tau s+1}\cdot \frac{1}{s}

2. The attempt at a solution
I know:
L^{-1}(\frac{1}{\tau s+1})=\frac{1}{\tau}e^{\frac{-t}{\tau}}
and:
L^{-1}({\frac{1}{s}})=1

But how to continue?
 
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Factor tau out of the denominator of the first fraction in Y(s) and use partial fraction expansion to break Y(s) into the sum of two simple fractions.
 
Awesome, thanks a lot!
 

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