How do I evaluate the integral [math]\int_{0}^{ \infty } \frac{ze^{-z}}{\sqrt{1-e^{-2z}} \mathrm{d} z [/math]?
How do I evaluate the integral [math]\int_{1}^{\infty}\frac{P(x)}{x+\frac{1}{2}} {dx}[/math] when [math]P(x)=x-\left \lceil x \right \rceil -\frac{1}{2}[/math]?