Please help me in finding Inverse Laplace transform of : $$ \frac{a(s^{2}-a^{2})}{s^4+4a^{4}} $$
I have tried id by following ways but need help in further approach
$$ splitting\ \ \ s^4+4a^4=(s^2+2as+2a^2)(s^2-2as+2a^2)\\and\\tried\ using\ partial\ fractions\ to\ solve\ the\ problem $$
But was not able to solve please HELP!
Hint.
$$ \frac{1}{((s+a)^2+a^2)((s-a)^2+a^2)} = \frac{c_1+c_2s}{(s+a)^2+a^2}+\frac{c_3+c_4s}{(s-a)^2+a^2} $$
then as
$$ \mathcal{L}^{-1}\left(\frac{\mu_1+\mu_2 s}{(s\pm a)^2+a^2}\right) = \frac{e^{\mp a t} \left(\left(\mu _1\mp a \mu _2\right) \sin (a t)+a \mu _2 \cos (a t)\right)}{a} $$
and
$$ s^n \hat f(s)\leftrightarrow\frac{d^n}{dt^n}f(t) $$
we are done.