How would you solve this integral?

[Dell]

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=e^t
dt=dx/x

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

 

[CompuChip]

When I plug it into Mathematica, I get
LogIntegral[x]
as the answer.

So I think there is no closed form.

 

[Dell]

if so could you please take a look at the following thread, it is where the integral came from, thanks
https://www.physicsforums.com/showthread.php?t=307749

 

[elect_eng]

$$\int$$((e^t)/(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.

$$=ln(t)+t+{{t^2}\over{(2)\;2!}}+{{t^3}\over{(3)\;3!}} + ...$$