• Support PF! Buy your school textbooks, materials and every day products Here!

How would you solve this integral?

  • Thread starter Dell
  • Start date
  • #1
590
0
how would you integrate the following, seemingly simple, function.

f(x)=1/ln(x)

what i tried to do was substitution
t=ln(x)
x=et
dt=dx/x

but from here i get to an integral of [tex]\int[/tex]((et)/(t))dt, no idea how to continue, tried integration in prts but keep going in cirlces, can anyone see how to do this?
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
When I plug it into Mathematica, I get
LogIntegral[x]
as the answer.

So I think there is no closed form.
 
  • #3
590
0
  • #4
364
2
[tex]\int[/tex]((et)/(t))dt, no idea how to continue, tried integration in prts but keep going in cirlces, can anyone see how to do this?
My integral table has this, but it is a series solution.

[tex] =ln(t)+t+{{t^2}\over{(2)\;2!}}+{{t^3}\over{(3)\;3!}} + ...[/tex]
 

Related Threads for: How would you solve this integral?

Replies
5
Views
961
  • Last Post
Replies
23
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
968
Replies
1
Views
2K
  • Last Post
Replies
2
Views
416
Replies
6
Views
535
Replies
6
Views
641
Top