Find the Laplace transform of (a) f(t) = e2t cosh² t (b) f(t) = tsin 6t (c) t³8 (t-1) Given the piecewise continuous function f(t) = 1, 0, e-4t, 0 < x < 2, 2 < x < 4, t> 4. (a) Express the above function in terms of unit step functions. (b) Hence, find the Laplace transform of f(t)