No, it's completely against my philosophy to memorize things just to remember; and things like Laplace transforms you look up in 'Beta: mathematics handbook' which you're typically allowed to bring to tests in engineering and in applied physics, at least here in Sweden.
What I mean is that if you know calculus you can do it fluently, like a language. You don't remember the solution, you calculate it, preferably in your head.
Edit: Though, back at my university tests took five hours, and I understand one or two hours is normal in America, and I could imagine that those shorter tests mean that there's more memorization and less sensible study.
It's acceptable to look things up that don't matter.
The way I see it, you should have the machinery in your head, so that you can derive things if pressed, and you should have the ability to work largely in your head and actually ponder things, but you shouldn't necessarily memorize formulas.
For example, I haven't even memorized the formula for the quadratic equation, I just complete the square in my head every time.
I think it's important to end up knowing them and to end up being able to calculate with paper and pencil to some degree and because calculus is very basic it's something one should be able to do in that way.
You should be able to imagine a right angle triangle sitting on the hypotenuse of another right angled triangle and figure out the x and y coordinates of the corner and how to get the sum of angles formulas from that, or to in general imagine things from calculus, like how the product rule can move what what is differentiated from one function to another etcetera.
What I mean is that if you know calculus you can do it fluently, like a language. You don't remember the solution, you calculate it, preferably in your head.
Edit: Though, back at my university tests took five hours, and I understand one or two hours is normal in America, and I could imagine that those shorter tests mean that there's more memorization and less sensible study.