∫x﹙arctanx﹚²dx=?
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![∫x﹙arctanx﹚²dx=?](/uploads/image/z/7018211-11-1.jpg?t=%E2%88%ABx%EF%B9%99arctanx%EF%B9%9A%26%23178%3Bdx%3D%3F)
∫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