My issue with both this and u-substitution is that you don't know what expression to use. There are a LOT of expressions that plausibly simplify the integral. But you have to do a bunch of algebra for each one (and not screw it up!), without really knowing whether it actually helps.
OTOH, if I'm given the expression, it's just mechanical and unrewarding.
OTOH, if I'm given the expression, it's just mechanical and unrewarding.