Hey can all work be clear and legible! Thank you!

1. Find the Laplace transform of the following functions using the table of transforms and the properties: (1) f(t) = the 2t + eff cost (2) f (t) = 7t sin (2t) 2. Use the definition of the Laplace transform to compute: L{t3 } 3. Determine the inverse Laplace transform of 8s - 2s- - 14 F (S) - (s + 1 ) (s2 - 2s + 5) 4. Solve the IVP using the method of Laplace transform: y" + 6y = t- - 1; v(0) =0. y'(0) = -1 5. What is the Laplace transform of the function Ost-1 f (t) 1