Series are of different types. For small values of x we use Taylor series. For large values we use Asymptotic expansions and Series that are expanded around infinity.

1) You could try to evaluate the integral using Romberg or Gaussian integration.

2) You truncate the various series expansions producing smaller approximations.

3) You look up the values in tables.

I have used the second one to come up with an example:

When x>=500.

Yes, but first I need that information from you.

1) Li(x), how big is x?

2)How many digits do you require because the answer is going to be in floating point.

Depends on the arguments or how much accuracy you need. There are several ways for each.

You can use the series given at http://en.wikipedia.org/wiki/Logarithmi … esentation