The phrase in the end means "finally". It is normally used when you want to give the impression that a conclusion was arrived at after a lot of confusion or uncertainty.

For example:

In the end, the hero runs away with all the money.

At the end, on the other hand, means at the point when something stops. Here we are thinking of a single event, and not a series of events. Take, for example, the following sentence:

At the end of the song, the hero jumps into the river.

The single event that we are thinking of here is the end of the song. When we say "in the end", what we have in mind is a sequence of events, not just one event. You cannot say "in the end of the song".

Here are a few more examples.

At the end of the third day, the little boy ran away.

In the end, the little boy runs away.

It's wrong to say in the end of... It should always be phrased as at the end of.

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