u-du or parts

[COCoNuT]

when doing integration, how do you know if you should use u-du substitution or integration by parts if the problem doesnt state it?

[Muzza]

Hopefully, you'll learn to "see" what to use after a while. Otherwise, first trying substitution and then (if that doesn't work) integration by parts often works...

[Tide]

Your basic strategy is to cast the integral into a familiar form. Sometimes it's obvious that one part of the integrand is the derivative of another part and other times it's obvious that a transformation will cast the integrand into something familiar. Otherwise, most of us try one then the other to see whether it leads anywhere. And sometimes neither one works!

I.e. there is no one size that fits all - which is why your calculus classes attempt to fill up your toolchest with as many tools as possible!