What is the value of ∫0∞arctan(x)x(1+x2)dx\int_0^{\infty} \frac{\arctan(x)}{x(1+x^2)} dx∫0∞x(1+x2)arctan(x)dx?
π24\frac{\pi^2}{4}4π2
ln2\ln 2ln2
π4\frac{\pi}{4}4π
π28\frac{\pi^2}{8}8π2