<b>1.</b> <i>Does the following integral converge ?</i><br><br>

$$\int_0^\infty \frac{b(x)}{B(x)} dx$$

<i>where</i>

$$b(x) = \sum_{n=1}^\infty \frac{n^x}{n^n} \qquad and \qquad B(x) = \sum_{n=1}^\infty \frac{n^x}{n!}$$

<br><b>2.</b> <i>Does it possess a closed form, or some other alternative expression ?</i>