anonymous
  • anonymous
What is the integral of 1/ln(x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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experimentX
  • experimentX
i suppose the integral cannot be expressed in elementary fuctions
anonymous
  • anonymous
No sir
experimentX
  • experimentX
looks like you know the answer ... care to share?

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More answers

anonymous
  • anonymous
It's li(x) which is called the logarithmic integral function, but I have no idea what it looks like and how to manipulate it.
experimentX
  • experimentX
li(x) is a special function not elementary function.
anonymous
  • anonymous
If you type this into wolfram alpha this is what pops up, but I've never seen it before.
anonymous
  • anonymous
Does any body know how to prove this or explain how it is derived.
anonymous
  • anonymous
Probably not huh?
experimentX
  • experimentX
It can't be derived ... try to understand, it's a special function like gamma function or beta function. http://en.wikipedia.org/wiki/Nonelementary_integral if you have some bounds then for some bounds, you really have nice expression in elementary terms.
anonymous
  • anonymous
Can you direct me to a link where I can read about special functions. Because I have the same trouble when dealing with the error function and gamma function
experimentX
  • experimentX
this is a good book but way too advanced for beginners http://www.amazon.com/Special-Functions-Z-X-Wang/dp/997150667X just refer to your calculus book http://books.google.com/books/about/Calculus.html?id=jBD0yTh64wAC&redir_esc=y
amistre64
  • amistre64
dy/dx = 1/ln(x) let y represent a power function perhaps ... y = S0 an x^n y' = S1 an n x^(n-1)\[\sum_1a_n~n~x^{n-1}=\frac1{ln(x)}\]
anonymous
  • anonymous
I have no idea what this means. I need to review power series especially Taylor series it seems.
anonymous
  • anonymous
Thanks guys especially experimentX
experimentX
  • experimentX
you can always represent an integral ... even if it's special function as power series. but for this particular case, expanding at x=0 is a bad idea ... for 0 is branch point with singularity.
experimentX
  • experimentX
you might want to try something like http://www.wolframalpha.com/input/?i=expand+1%2Flog%28x%29+at+x%3D1 or expand series at some other point and integrate term by term.

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