When asked to find the antiderivative of an expression involving familiar functions, we often have an idea of what the answer might be. We can then check and correct our guess by taking the derivative. This "advanced guessing" is related to the technique called "substitution", in which we attempt to simplify the integrand as a step toward finding the derivative.
Lecture Video and Notes
Antidifferentiation by Substitution
Antiderivative of tan x sec2x