Determine whether $\int_0^{\infty} \frac{\arctan(x)}{e^x - e}dx$ converges or diverges.
Attempt: I know that $\arctan x\leq \pi/2$, but how can I proceed from here? I also split the integral as:
$\int_0^{\infty} \frac{\arctan(x)}{e^x - e}dx$=$\int_0^{1} \frac{\arctan(x)}{e^x - e}dx$+$\int_1^{\infty} \frac{\arctan(x)}{e^x - e}dx$