If I'm not mistaken, the TI derivative/anti-derivatives solving methods rely on approximations when the answer can't be obtained by the logic programmed into these methods.
In other words, where there's insufficient logic programmed, the TI cranks out an approximation, then based on user input, makes an extremely educated guess as to what the "exact" answer is.
I would think that guess is better than nearly all humans could make, and was necessary because nearly all humans can't program sufficient logic to come up with the dx or anti-dx for every possible expression.
