Explanation of #32 in the Laplace Transform Table

#32 involves the integral of an auxiliary function, f(v).

It says that
1) if we have to find the Laplace transform of a function, g(t), which is the result of the integral of a second function, f(v)

2)

then we can get the transform of the first function by taking the Laplace transform of the second function (the one under the integral sign) and substitute it on the right-hand side of #32.

So the steps needed are to find a function f(v) and then its transform. The final step is to substitute these results on the right-hand side.