find the laplace transform of f(t) when:
f(t)= 9 , 0 = or < t < 2
f(t)= (t-5)^2 , 2= or < t < 5
f(t)= 2te^6t , t > or = 5

and presumably 0 for . We can express in terms of the unit step function,

Quick explanation: for , and for . So subtracting these will cancel the value of 9 for all and leave us with the value of 9 over the interval we want, . The same reasoning applies for the other 3 terms.

Recall the time displacement theorem:

By this property, we have

Putting everything together, we end up with