How to find Laplace Transform of some Functions

As we saw in the last section computing Laplace transforms directly can be fairly complicated. Usually we just use a table of transforms when actually computing Laplace transforms. The table that is provided here is not an all-inclusive table but does include most of the commonly used Laplace transforms and most of the commonly needed formulas pertaining to Laplace transforms.
Before doing a couple of examples to illustrate the use of the table let’s get a quick fact out of the way.
Given f(t) and g(t) then,
L{af(t)+bg(t)} = aF(s)+bG(s)
for any constants a and b.
In other words, we don’t worry about constants and we don’t worry about sums or differences of functions in taking Laplace transforms. All that we need to do is take the transform of the individual functions, then put any constants back in and add or subtract the results back up.
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