$($a$)$ Using the definition of the Laplace Transform, find $L(f(t))$ where:

$f(t)=t0t<mn>1</mn>$

$=1t1$

$($b$)$ Find the Laplace transform of:

$t^3$exp$(-2t)$

exp$(-2t-5)$

texp$(-6t)$

$($c$)$ Find the Inverse Laplace transform of:

$\frac{1}{s^2+5s}$

$\frac{4}{s^2-6s+25}$