Calculate ∫01x2arctanx1+x2dx\int_{0}^{1} \frac{x^2 \arctan x}{1+x^2} dx∫011+x2x2arctanxdx.
π8−14ln2\frac{\pi}{8} - \frac{1}{4} \ln 28π−41ln2
π216−12ln2\frac{\pi^2}{16} - \frac{1}{2} \ln 216π2−21ln2
π4−12ln2\frac{\pi}{4} - \frac{1}{2} \ln 24π−21ln2
π232−12ln2\frac{\pi^2}{32} - \frac{1}{2} \ln 232π2−21ln2