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## Main Question or Discussion Point

How do you integrate (ln ln x)^n for any n?

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How do you integrate (ln ln x)^n for any n?

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nicksauce

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Well since mathematica isn't able to find a formula for n=2, I'm going to say "numerically".

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What do you mean exactly by "numerically"? Do you mean that i should evaluate it as a definite integral?Well since mathematica isn't able to find a formula for n=2, I'm going to say "numerically".

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nicksauce

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[tex]\int[/tex]-log[-log[x]]dx=Euler Constant (.577...)

This follows from differentionation the gamma function in its product and integral forms and making a change of variables.

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Although this method would be painful, since I cannot express this integral in terms of elementary functions, could I represent (ln ln x)^(n) as a Taylor polynomial (what is the Taylor series for ln ln x, anyways?) and then integrate that and leave it as a Taylor Series?

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