Integration - antidifferentiation (finding the original function)

What function has the derivative  ?

What function could have been differentiated to give the result ?

Here are some possibilities:

There is an infinite family of such functions. To represent this situation, include the constant of integration.

Finding the original function is the reverse process of differentiation.

Working in pairs:

• each person chooses a function and differentiates
• swap derivatives and find the original function (ignoring any constant).

Can you suggest any rules for finding the original function?