What is integration by parts rule? How does ILATE rule come?

Statement 1: int(dx)/(x^(3)sqrt(1+x^(4)))=-(1)/(2)sqrt(1+(1)/(x^(4)))+C Statement 2: For integration by parts,we have to follow ILATE rule

Integration by Substitution and By parts | ILATE Formula

Integration By parts : ILATE || How to judge u & v || Successive Integration || Important Questions OF IBP

Which does not obey EAN rule?