Integrate (ln ln x)^n

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

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  • #2
nicksauce
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Well since mathematica isn't able to find a formula for n=2, I'm going to say "numerically".
 
  • #3
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Well since mathematica isn't able to find a formula for n=2, I'm going to say "numerically".
What do you mean exactly by "numerically"? Do you mean that i should evaluate it as a definite integral?
 
  • #4
nicksauce
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Well I just mean if you want to find a general closed for expression for the indefinite integral, you are out of luck. Therefore the only way I can conceive of doing an integral with this expression would be to do a definite integral numerically.
 
  • #5
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there is one place where the integral can be evaluated explicitly that I know of.
[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.
 
  • #6
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Well I just mean if you want to find a general closed for expression for the indefinite integral, you are out of luck. Therefore the only way I can conceive of doing an integral with this expression would be to do a definite integral numerically.
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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