∫x2arctanxdx
【正确答案】：∫x2arctanx=1/3∫arctanxdx3=1/3x3arctanx -(1/3)∫3darctax=(1/3)x3arctanx-1/3∫[x3/(1+x2)]dx =(1/3)x3arct-1/3∫[x(1+x2)-x]/(1+x2)dx =(1/3)x3arctan-(1/3)∫xdx+(1/3)∫[x/(1+x2)]dx =(1/3)x3arctanx-(1/6)x2+1/6∫d(1+x2/(1+x2)) =(1/3)x3arctanx-(1/6)x2+(1/6)ln(1+x2)+C．
