Question: Is there an example where the NO_INT option in invlaplace makes a difference?

In the help page for invlaplace we find the statement
"If the option opt is set to 'NO_INT', then the program will not resort to integration of the original problem if all other methods fail.  This will increase the speed at which the transform will run."

This statement is found in Maple 2017 and in Maple 8 and I believe in all versions in between.
Can anyone provide an example of a function F(s), where
invlaplace( F(s) ,s, t, NO_INT);
gives a different result (or works faster) than
invlaplace( F(s) ,s, t);
## It should be added that an identical statement is made in the help page for laplace itself.

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