Consider finding the inverse Laplace Transform of the function $P(s)=\frac{9s+1}{(s^2+25)(s+3)}.$ You are given that when partial fractions are applied to $P(s),$ it can be rewritten as $P(s)=\frac{\frac{13}{17}s+\frac{114}{17}}{s^2+25}-\frac{\frac{13}{17}}{s+3}.$ The inverse Laplace Transform of $P(s)$ is:

a$)p(t)=\frac{13}{17}cos(5t)+\frac{114}{85}sin(5t)-\frac{13}{17}{e}^{-3t}$

b$)p(t)=\frac{13}{17}tcos(5t)-\frac{114}{85}tsin(5t)-\frac{13}{17}{e}^{-3t}$

c$)p(t)=\frac{13}{17}cos(5t)-\frac{104}{85}sin(5t)-\frac{13}{17}{e}^{-3t}$

d$)p(t)=\frac{13}{17}cos(5t)-\frac{124}{85}sin(5t)+\frac{11}{17}{e}^{-3t}$

e$)$ None of the other options are correct