So far I've tried u-substitution and set the u = e^x - 1. This gave me the integral of 1/(1+u^2)du which is arctan(u) or arctan(e^x-1), then i set the pike from 0 to ln(2), but that just gave me arctan(3) - arctan(2) which isn't one of the answers, does anybody know what I did wrong?

What did you get when you set the limits? - show detailed work. Your integration is correct. We would not know "what you did wrong" - unless you show us your work regarding the limits.