Calculate $\int_{0}^{\infty}\frac{\arctan(x)}{(1+x^2)^{3/2}}dx$ or show that it diverges Calculate the following improper integral or show that it diverges. 
$$\int_{0}^{\infty}\frac{\arctan(x)}{(1+x^2)^{3/2}}dx$$
I'm really lost. Your help would be very appreciated. 

Sub $x=\tan{t}$ and the integral is equal to
$$\int_0^{\pi/2} dt \, t \, \cos{t} $$
Which may easily be evaluated by parts:
$$[ t \sin{t}]_0^{\pi/2} - \int_0^{\pi/2} dt \, \sin{t} = \frac{\pi}{2}-1 $$
