企源知识库

求∫x²arctanz
【正确答案】：∫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