Question

What is the integral of 1/ln(x)

Answer 1

i suppose the integral cannot be expressed in elementary fuctions

Answer 2

No sir

Answer 3

looks like you know the answer ... care to share?

Answer 4

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.

Answer 5

li(x) is a special function not elementary function.

Answer 6

If you type this into wolfram alpha this is what pops up, but I've never seen it before.

Answer 7

Does any body know how to prove this or explain how it is derived.

Answer 8

Probably not huh?

Answer 9

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.

Answer 10

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

Answer 11

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

Answer 12

dy/dx = 1/ln(x)

let y represent a power function perhaps ...

y = S0 an x^n
y' = S1 an n x^(n-1)\[\sum_1a_n~n~x^{n-1}=\frac1{ln(x)}\]

Answer 13

I have no idea what this means. I need to review power series especially Taylor series it seems.

Answer 14

Thanks guys especially experimentX

Answer 15

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.

Answer 16

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.