∫x﹙arctanx﹚²dx=?

∫x﹙arctanx﹚²dx=?
∫x﹙arctanx﹚²dx=?

∫x﹙arctanx﹚²dx=?
∫x(arctanx)²dx
=1/2∫(arctanx)²dx²
=1/2(xarctanx)²-∫(x²arctanx)/(1+x²)dx
=1/2(xarctanx)²-∫[arctanx-arctanx/(1+x²)]dx
=1/2(xarctanx)²-∫arctanxdx-∫arctanxd(arctanx)
=1/2(xarctanx)²-xarctanx+∫x/(1+x²)dx-1/2(arctanx)²
=1/2(xarctanx)²-xarctanx+1/2ln(1+x²)-1/2(arctanx)²+C