求∫x2arctanz
∫x2arctanxdx=1/3∫arctanxd(x3)=(1/3)x3•arctanx-1/3∫x3d(arctanx)=(1/3)x3•arctanx-1/3∫[(x3+x-x)/(1+x2)]dx=(1/3)x3•arctanx-1/3∫[xdx+1/6∫[1/(1+x2)]d(1+x)2=(1/3)x3•arctanx-(1/6)x2+(1/6)in/(1+x2)+C
求∫x2arctanz
∫x2arctanxdx=1/3∫arctanxd(x3)=(1/3)x3•arctanx-1/3∫x3d(arctanx)=(1/3)x3•arctanx-1/3∫[(x3+x-x)/(1+x2)]dx=(1/3)x3•arctanx-1/3∫[xdx+1/6∫[1/(1+x2)]d(1+x)2=(1/3)x3•arctanx-(1/6)x2+(1/6)in/(1+x2)+C
