Determine Whether the Improper Integral Converges or Diverges, and If $\int_{-\infty}^{\infty} \frac{3 e^{x}}{3+e^{2 x}} d x$

Multiple Choice

Determine whether the improper integral converges or diverges, and if it converges, find its value. $\int_{-\infty}^{\infty} \frac{3 e^{x}}{3+e^{2 x}} d x$

A) $\frac{\pi \sqrt{3}}{2}$
B) $\sqrt{3}$
C) $\frac{\pi \sqrt{3}}{3}$
D) Diverges