Need help with comparison method for improper integral?

[mottov2]

Homework Statement

$\int \frac{arctan(x)}{2+e^x}dx$
where the interval of the integrand is from 0 to infinity.

In order to use the comparison method I need to compare 2 functions but I am having so much difficulty figuring out what function to compare it to.

Its not just this particular question, any question asking to use comparison method, I can't seem to figure out the function to compare it to.

Can I get some tips to finding a function to compare it to?

 

[Char. Limit]

tan^-1(x) < 2 for all x, so therefore...

$$\frac{tan^{-1}(x)}{2 + e^{x}} < \frac{2}{2 + e^{x}}$$

for all x (Since 2+e^x is never 0, one doesn't have to worry about division by zero.)

So try using the comparison test with that.