Find the Laplace transform of the following functions:

a. \(f(t)=9 t^{2}-7\).

b. \(f(t)=e^{5 t-3}\).

c. \(f(t)=\cos 7 t\)

d. \(f(t)=e^{4 t} \sin 2 t\).

e. \(f(t)=e^{2 t}(t+\cosh t)\).

f. \(f(t)=t^{2} H(t-1)\).

g. \(f(t)=\left\{\begin{array}{cc}\sin t, & t<4 \pi \\ \sin t+\cos t, & t>4 \pi\end{array}\right.\).

h. \(f(t)=\int_{0}^{t}(t-u)^{2} \sin u d u\).

i. \(f(t)=(t+5)^{2}+t e^{2 t} \cos 3 t\) and write the answer in the simplest form.