I have a problem using the comparison test for integrals and I'm stuck. The question asks whether the integral of (arctanx)/(2+e^x) dx from 0 to infinity diverges or converges using the comparison test for improper integrals.

My reasoning is that you can ignore the arctanx since the max value of that is pi/2, so it's pretty much a constant so you take that out. Then compare 1/(2+e^x) to 1/(e^x) to see if that diverges. However, how do you find the integral of 1/(e^x) in order to see if it converges or diverges. Should I even compare the original with 1/(e^x)? Help please? Thanks.