determine if this is convergent or divergent? If convergent, find the value.

integral (from 0 to infinity) of e^x / (e^2x + 3)

Question

determine if this is convergent or divergent?  If convergent, find the value.

integral (from 0 to infinity) of e^x / (e^2x + 3)

anonymous · Answer

I was taught to break it into another integral from 0 to 'A', integrate, then see what happens when A goes to infinity, but I'm having trouble integrating it.

anonymous · Answer

because integral (from 0 to infinity) of e^x / (e^2x + 3) behaves like integral (from 0 to infinity ) of 1/ e^n. By the comparison test we know that ( integral from 0 to infinity e^-ax dx converges for a > 0 ) so we know that it converges for all n values greater than 0.

anonymous · Answer

how do I know that the original lies above 1/e^n?  I understand the comparison test, but I need to know that the original is above it if the known one diverges.