Math Subject GRE 1268 Question 55 If $a$ and $b$ are positive numbers, what is the value of $\displaystyle \int_0^\infty \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})}dx$.  
Tale $a = 1$ and let $b\to 0^+.$ In the limit you get
$$\int_0^\infty\frac{e^x-1}{(1+e^x)2}\,dx.$$
That integral equals $\infty$ because the integrand has a positive limit at $\infty.$ The only answer that fits this phenomenon is E.
