This is a bit of a strange pairing on the surface of it; the artificer is a very cerebral, scholarly class and the berserker is … not. However, inventive creativity is hardly a guarantee of a calm disposition, and a capacity for physical violence does nothing to stop a person from being able to study the necessary knowledge to create spell inventions. Still, this is an unusual combination to be sure, and those wanting to create a character that mixes these classes should give some thought to what that looks like.
Mechanically, this is not the most powerful, but it’s not too bad in terms of ability score spread. A berserker mostly wants strength and constitution, and an artificer really just needs intelligence. It’s probably best to figure out what priority those three ability scores have in relation to one another, but it’s far from unworkable. This is also helped along somewhat by the fact that the artificer class has a number of combatoriented archetypes.
More levels in berserker will give you a standard ball of fury and melee weapon skill with a bit of gadgeteering to hand as a back-up or force multiplier. More levels of artificer will give you a magical crafter and possibly warrior who can get in touch with their wrathful side when needed. A mix of the two is probably the most uncommon, and represents a fusion of ingenuity and raw violence who is probably rightly feared by those around them.
[[Synergy Feats for Multiclassers#Artificer w/ Berserker|Artificer-Berserker chains and ideas]]