∫x﹙arctanx﹚²dx=？
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∫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
=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
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