find the inverse laplace of 1/((s^2+8s+17)(1+e^(-pi*s)))

here second shifting can be applied but how as e^(-pi*s) is in the denominator

please help

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- Mar 5th 2013, 03:54 AMprasuminverse laplace
find the inverse laplace of 1/((s^2+8s+17)(1+e^(-pi*s)))

here second shifting can be applied but how as e^(-pi*s) is in the denominator

please help - Mar 5th 2013, 11:23 AMBobPRe: inverse laplace
You have to expand

$\displaystyle \frac{1}{(1+e^{-\pi s})}$

as an infinite series. - Mar 6th 2013, 04:50 AMprasumRe: inverse laplace
what is the expansion series of 1/(1+e^-x)

- Mar 6th 2013, 09:48 AMBobPRe: inverse laplace
Make use of the binomial expansion,

$\displaystyle \frac{1}{1+x}=1-x+x^{2}-x^{3}+x^{4}- \dots.$