Evaluate this integral:
$$ \large \int_0^\infty\frac1{x^x}dx $$

Question

experimentx · Answer

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turingtest · Answer

$$\large \int_0^\infty\frac1{x^x}dx$$learn latex!

experimentx · Answer

yeah i know ... draw is just too quicker.

anonymous · Answer

I doubt you can define it.  The lower bound is an essential singularity.

experimentx · Answer

anonymous · Answer

@experimentX  can u solve this.

experimentx · Answer

anonymous · Answer

Huh, interesting.  Well, I would take a look in Gradshteyn and Ryzhik.  If it can be defined at all, even as a series, it will be there.

experimentx · Answer

i hope so!!

anonymous · Answer

santosh just like that integral

$$ \int_0^\infty\frac1{x^x}dx=\sum_{n=0}^{\infty} \frac{(-1)^n}{n!} \int_{-\infty}^{\infty} t^n e^{(n+1)t} dt$$

anonymous · Answer

but the later integral part diverges

experimentx · Answer

yep ... this isn't analytic :((

anonymous · Answer

try it with mathematica...in terms of n and t

anonymous · Answer

Hmm, if you plot the integrand it seems perfectly well-behaved over the entire domain.

experimentx · Answer

@Carl_Pham it converges ... 
@mukushla that's one hell of crazy structure :(((

anonymous · Answer

@experimentX please tell me how |dw:1345409192350:dw|