Determine whether the integral converges or diverges, and find its value if it converges.
This function is definitely weird at 0. We break up the integral into two pieces, splitting the interval at x = 0:
Let's integrate the one with non-negative limits of integration first, since this integral looks more likely to diverge and save us work.
As b approaches 0 the quantity approaches ∞, which means e1/b approaches ∞ also. This integral diverges, which means the original integral diverges. We don't have to bother with the other integral.