Determine whether or not the improper integral from 0 to infinite of (e^x)/[(e^2x)+4] converges and if it does, find it's definite value.
The Attempt at a Solution
I missed the lecture on the Comparison Test, so I'm essentially useless.
I assign g(x) = e^x. Let f(x) be the function defined in the question statement. g(x) > f(x) on 0 to infinite, so if g(x) converges then f(x) converges, correct? I then sub in t as the upper limit and evaluate the function as t approaches infinite. This limit cannot be evaluated, so g(x) converges and therefore f(x) converges, right?
Thanks for any help.