为自己加油

∫x²arctanxdx

∫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．