$$\mathcal{L}^{- 1} \left( \frac{ (p + 1) e ^{- \pi / p}}{p ^ 2 + p + 1}\right) $$
I have already solved the question in which exponential power was $-\pi p$ instead of $-\frac{\pi}{p}$. The latter factor is disturbing me. I have also solved the whole part of the question except the exponential part.
But neither I know how to apply the shift theorem further nor find its Heaviside unit step function.
So, how should I proceed further?