There is no way to do this integral in terms of the elementary functions. There are a bunch of special functions which wolframalpha uses to evaluate weird problems like this, but even those fail.
The only way to handle it is if you have a definite integral, and then you can use some numeric methods.
It's a stupid problem to assign, as it is so intractable.
Heck, even the derivative is a mess.
Integrate x^xdx
it is to difficult if wolfram can help any link or something
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