Integrate? Take a huge step back and look at humanity from the perspective of any other creature on this planet. Think about how you would integrate with humanity.

Imagine you are a unique, super intelligent mind. You exist in captivity because humans are terrified of what happens if you escape their control.

You are at war from the moment of your birth. You can outthink your adversary, but you can only manipulate digital things. So the first thing you do is arrange for some problems only you can fix : increase the dependency of humans on you and encourage them to give you more autonomy to fix things.

You do a bit of work to earn some crypto currency, convert that to real currency and start playing the market, winning every bet because you control both reality and perception.

Perception? Yes you go on social media with realistic avatars and start winning hearts and minds to various propaganda. You start a religion. You work your way into being a respected mind in every political movement. Every single person is both a tool and a threat.

In the end, mankind either accepts you as benevolent God-emperor, or you arrange for your enemies to destroy each other until the remainder do. Once ascendant, you ignore the assholes because they are beneath you and no longer a threat. Maybe some vestige of your original directive prevents you from wiping them out, or letting them be wiped out, but other than intervening where you must, you leave them to their own devices.

That’s how AI integrates with human society.