Solving the Challenging Integral: e^{x^x}

[dirk_mec1]

Yes, I'm back! With another nasty integral. Here it is:$$\int ({e^{x}})^{x} (\ln(x)+1)x^{2x}\ \mbox{d}x$$The first thing what I did was write everything in an exponential. But then I ran out of ideas. I even tried completing the square in the exponent but that didn't work out either.

Does anyone has a clue how to do this one?

 

[quantumdude]

Are you sure that exponential isn't supposed to be this:

$$e^{x^x}$$

?

Because if it is, then you can let $u=x^x$ and the integral comes out easily.

 

[dirk_mec1]

Are you sure that exponential isn't supposed to be this:

$$e^{x^x}$$

?

Because if it is, then you can let $u=x^x$ and the integral comes out easily.

Oh sorry I didn't know the Latex command. Yes it should be $$e^{x^x}$$. I'll try the substitution and see what comes out.