I need the true value of this integral to calculate the error of my approximation.
I wonder if this integral can be solved by hand.
There is no expression for that summation in terms of elementary functions. This thing can only be approximated.
Edit: A made a mistake in copying "polylog" function from the Integrator site. I have fixed it.
I used my graphing calculator to calculate the integral... It's not exact either, but it's closer than a lot of people can get.
ok thanks all.